.

Метод p-аналітичних функцій в крайових задачах для еліптичних систем диференціальних рівнянь: Автореф. дис… канд. фіз.-мат. наук / І.В. Клен, Київ.

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130 1988
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EE?ANUeEEE OI?AA?NEOAO ?iai? OA?ANA OAA*AIEA

EEAI ??EIA A?EOI??AIA

OAeE 517.9:517.544

IAOIAe p-AIAE?OE*IEO OOIEOe?E

A E?AEIAEO CAAeA*AO AeEss AE?IOE*IEO NENOAI

AeEOA?AIOe?AEUeIEO ??AIssIUe

01.01.02 — aeeoa?aioe?aeuei? ??aiyiiy

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

EE?A–1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia ia eaoaae?? iaoaiaoe/ii? o?ceee Ee?anueeiai oi?aa?neoaoo
?iai? Oa?ana Oaa/aiea.

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

i?ioani? ,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea,

i?ioani? eaoaae?e iaoaiaoe/ii? o?ceee;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

i?ioani? Aeouaiei Aiae??e A?naiiae/,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea,

i?ioani? eaoaae?e iaoaiaoe/ii? o?ceee.

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

i?ioani? A??/aiei I?ia Iiaian?aia,

Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie “EI?”,

i?ioani? eaoaae?e aeui? iaoaiaoeee ? 1;

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe,

aeioeaio sseiaaiei Aaneeue Iaeneiiae/,

Iaoe?iiaeueiee aa?a?iee oi?aa?neoao,

aeioeaio eaoaae?e aeui? iaoaiaoeee.

I?ia?aeia onoaiiaa: ?inoeooo iaoaiaoeee IAI Oe?a?ie, a?aeae?e
iaoaiaoe/ii? o?ceee ? oai??? iae?i?eieo eieeaaiue (i. Ee?a).

Caoeno a?aeaoaeaoueny “24” o?aaiy 1999 ?. i 14.00 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.001.37 i?e Ee?anueeiio oi?aa?neoao?
?iai? Oa?ana Oaa/aiea (252127, i. Ee?a–127, i?-o Aeooeiaa, 6,
iaoai?ei-iaoaiaoe/iee oaeoeueoao).

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea ca aae?anith: i. Ee?a,
aoe. Aieiaeeie?nueea, 58.

Aaoi?aoa?ao ?ic?neaiee “6” ea?oiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Iieey/oe I.I.CAAAEUeIA
OA?AEOA?ENOEEA

Aeooaeuei?noue oaie. Oi/i? aiae?oe/i? ?ica’ycee e?aeiaeo caaea/ aeey
aeeoa?aioe?aeueieo ??aiyiue iathoue aaeeea cia/aiiy, aeath/e oe?ieo
iiaeeea?noue aeey oai?aoe/ieo aeine?aeaeaiue, a oaeiae aenooiath/e ye
oanoia?, aeey ioe?iee yeino? iaaeeaeaieo iaoiae?a. Eean e?aeiaeo caaea/,
ui iathoue oi/i? ?ica’ycee, aeey aeeoa?aioe?aeueieo ??aiyiue c? ci?iieie
eiao?oe??ioaie aeineoue aocueeee. Iaoiae ocaaaeueiaieo aiae?oe/ieo
ooieoe?e, cie?aia, p-aiae?oe/ieo ooieoe?e, yeee ? ocaaaeueiaiiyi iaoiaeo
ne?i/aiieo ?ioaa?aeueieo ia?aoai?aiue, aeicaiey? ?icoe?eoe oeae eean.

Iiaeeea?noue ca’ycaoe oai??th aiae?oe/ieo ooieoe?e c ae?ioe/iith
nenoaiith ??aiyiue c /anoeiieie iio?aeieie aoea iii?/aia A. I?ea?ii ua a
1891 ?. ?ioa?an aei oe??? ?aea? aeiee eeoa a OO no. Na?ae/aiiyi oiai ?
?iaioe ?.I.Aaeoa, A.I.Iieiae?y, E.Aa?na oa A.Aaeueaa?oa.

Iaeia c ocaaaeueiaiue oai??? aiae?oe/ieo ooieoe?e eiiieaenii? ci?iii? –
oea oai??y p-aiae?oe/ieo ? (?, q)-aiae?oe/ieo ooieoe?e, yea ?ic?iaeaia
A.I. Iieiae??i ? aeeeaaeaia a eiai iiiia?ao?yo. p-aiae?oe/i? oa (?,
q)-aiae?oe/i? ooieoe?? ciaeoee oe?iea canoinoaaiiy i?e ?ica’ycaii?
caaea/ iaoai?ee nooe?eueieo na?aaeiaeu, aiie iia’ycai? c oaeeie
aaaeeeaeie caaea/aie o?ceee oa iaoai?ee ye caaea/? aeaeo?inoaoeee oa
iaai?oinoaoeee, caaea/? oai??? o?eueo?aoe??, caaea/? a?ae?iiaoai?ee
?aeaaeueii? oa a’ycei? ianoeneeai? ??aeeie, caaea/? i?i aaciiiaioiee
iai?oaeaiee noai iaieiiie iaa?oaiiy, caaea/? i?i iai?oaeaiee noai
e?oaiai? neiao??? o?e, i?inoi?ia? iaa?naneiao?e/i? caaea/? oai???
i?oaeiino?, a?naneiao?e/i? caaea/? oai??? iioaioe?aeo, caaea/? e?o/aiiy
o?e iaa?oaiiy oa ?io.

sseui oai??y ocaaaeueiaieo aiae?oe/ieo ooieoe?e, cie?aia, p-aiae?oe/ieo
ooieoe?e, a iniiaiiio aaea iiaoaeiaaia, oi iaoiaee ?ica’ycaiiy e?aeiaeo
caaea/ aeey ocaaaeueiaieo aiae?oe/ieo ooieoe?e, cie?aia, p-aiae?oe/ieo
ooieoe?e aeey eiie?aoieo oa?aeoa?enoee ?=p(o) ua aeaeae? a?ae
aeineiiaeino?. Oiio ?ic?iaea iiaeo aoaeoeaieo iaoiae?a ?ia’ycaiiy
e?aeiaeo caaea/ ocaaaeueiaieo aiae?oe/ieo ooieoe?e ?, cie?aia,
?-aiae?oe/ieo ooieoe?e noaiiaeoue aaaeeeao e aeooaeueio i?iaeaio.

Iaeia c a?aeiieo iaoiaeee ?ica’ycaiiy e?aeiaeo caaea/ ?-aiae?oe/ieo
ooieoe?e aaco?oueny ia aeei?enoaii? ?ioaa?aeueieo cia?aaeaiue oeeo
ooieoe?e /a?ac a?aeiia?aei? aiae?oe/i? ooieoe?? eiiieaenii? ci?iii?.
Oaea ?ioaa?aeueia cia?aaeaiiy aeey ?-aiae?oe/ieo ooieoe?e c
oa?aeoa?enoeeith ?=ok (k=const>0), a?aeiia a e?oa?aoo?? ye iniiaia
?ioaa?aeueia cia?aaeaiiy ok-aiae?oe/ieo ooieoe?e, anoaiiaeaii
A.I. Iieiae??i. Aeei?enoaiiy ?ioaa?aeueieo cia?aaeaiue
?-aiae?oe/ieo ooieoe?e /a?ac aiae?oe/i? ooieoe?? aeicaiey? caiaeeoe
?ica’ycaiiy e?aeiaeo caaea/ ?-aiae?oe/ieo ooieoe?e aei
?ica’ycaiiy e?aeiaeo caaea/ aiae?oe/ieo ooieoe?e, aeineoue aeia?a aaea
aea/aieo. Aeacaia iaoiaeeea aeey ?ica’ycaiiy e?aeiaeo caaea/
ok-aiae?oe/ieo ooieoe?e cai?iiiiiaaia A.I. Iieiae??i. Iiaeaeueoee
?icaeoie aiia iaea?aeaea a ?iaioao A.I. Iieiae?y, I.I. Eaioeaiai oa ?o
o/i?a aieiaiei /eiii noiniaii aei e?aeiaeo caaea/ o-aiae?oe/ieo
ooieoe?e. Oey iaoiaeeea aeei?enoiaoaaeanue i?e ?ica’ycaii? e?aeiaeo
caaea/ o-aiae?oe/ieo ooieoe?e, ui a?aeiia?aeathoue a?naneiao?e/iei
caaea/ai oai??? i?oaeiino? oa caaea/ai a?ae?iiaoai?ee a’ycei?
ianoeneeai? ??aeeie, oa e?aeiaeo caaea/ ?-aiae?oe/ieo ooieoe?e c ?ioeie
oa?aeoa?enoeeaie.

Iaoiaee, ye? aacothoueny ia ?ioaa?aeueieo cia?aaeaiiyo, ui ca’ycothoue
a?naneiao?e/i? aa?iii?/i? ooieoe?? c ieineeie aa?iii?/ieie ooieoe?yie
aai c aiae?oe/ieie ooieoe?yie, aeei?enoiaoaaeenue i?e ?ica’ycaii?
a?naneiao?e/ieo caaea/ oai??? iioaioe?aeo ? oai??? i?oaeiino? aeaaii.
I?eeeaaeii oiio ? ?iaioe N. Aaaa?a, O. Iaea?a, A.ss.
Aeaenaiae?iaa, TH.?. Nieia’eiaa oa ss.N. Ooeyiaea.

Aiae?c ?acoeueoao?a ?ia?o ii ?ica’ycaiith e?aeiaeo caaea/ ?-aiae?oe/ieo
ooieoe?e, cie?aia, a?naneiao?e/ieo e?aeiaeo caaea/ oai??? iioaioe?aeo oa
oai??? i?oaeiino?, oeyoii caaaeaiiy ?o ca aeiiiiiaith ?ioaa?aeueieo
cia?aaeaiue aei e?aeiaeo caaea/ aiae?oe/ieo ooieoe?e iieaco?, ui oey
iaoiaeeea aoaeoeaia, yeui e?aeiao caaea/o aaea?oueny caanoe aei oaei?
e?aeiai? caaea/? aiae?oe/ieo ooieoe?e, ?ica’ycie yei? ia o?eueee
caieno?oueny a eaaae?aoo?ao, aea e ii iiaeeeaino? a iaea?eueo i?ino?e
oi?i?. A /a?ac oa, ui oea aaea?oueny c?iaeoe eeoa aeey i?inoeo iaeanoae
(? oi ia caaaeaee), oi e aoaeoeai?noue iaoiaeeee ia aeineoue aeniea.
Iiooee iiaeeeainoae i?aeaeuaiiy aoaeoeaiino? oe??? iaoiaeeee iieacaee,
ui oeueiai iiaeia aeinyaoe ca ?aooiie i?iaaaeaiiy aeeaieeo
aeine?aeaeaiue aia?aoieo oa ye?nieo aeanoeainoae aeei?enoiaoaaieo
?ioaa?aeueieo cia?aaeaiue. Ii/aoie nenoaiaoe/iei aeine?aeaeaiiyi a
oeueiio iai?yieo i?e ?ica’ycaii? e?aeiaeo caaea/ o-aiae?oe/ieo ooieoe?e
iieeaaeaii a ?iaioao A.I. Iieiae?y oa I.I. Eaioeaiai, i?e ?ica’ycaii?
e?aeiaeo caaea/ ok-aiae?oe/ieo ooieoe?e – a ?iaioao I.I. Eaioeaiai oa
eiai o/i?a. ?ioaa?aeuei? cia?aaeaiiy o-aiae?oe/ieo ooieoe?e /a?ac
a?aie/i? cia/aiiy aiae?oe/ieo ooieoe?e iaea?aeaii a ?iaioao I.I.
Eaioeaiai, a cia?aaeaiiy ok-aiae?oe/ieo ooieoe?e – a ?iaioao
I.I. Eaioeaiai oa aaoi?a. Oeeie ?iaioaie ?icaeoie iaoiaeeee ?ica’ycaiiy
e?aeiaeo caaea/ ?-aiae?oe/ieo ooieoe?e ca aeiiiiiaith ?o ?ioaa?aeueieo
cia?aaeaiue /a?ac a?aie/i? cia/aiiy aiae?oe/ieo ooieoe?e i?aeiyoi ia
ye?nii iiaee ??aaiue.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Oaiaoeea
aeena?oaoe?eii? ?iaioe a?aeiineoueny aei ieai?a iaoeiaeo aeine?aeaeaiue
eaoaae?e iaoaiaoe/ii? o?ceee Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana
Oaa/aiea, a oaeiae iia’ycaia c iaoeiai-aeine?aeiith aea?aeathaeaeaoiith
oaiith “Aeine?aeaeaiiy iae?i?eieo e?aeiaeo caaea/ iaoaiaoe/ii? o?ceee c
canoinoaaiiyi a aeooaeueieo iaeanoyo iaoai?ee nooe?eueiiai na?aaeiaeua ?
o?ceee” (? 533, 1992–1993 ??.).

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith ?iaioe ? ?ic?iaea iiai? aoaeoeaii?
iaoiaeeee ?ica’ycaiiy e?aeiaeo caaea/ aeey ae?ioe/ieo nenoai
aeeoa?aioe?aeueieo ??aiyiue ia iniia? iaoiaeo ?-aiae?oe/ieo ooieoe?e
(p=ok, k=const>0), ca aeiiiiiaith ?ioaa?aeueieo cia?aaeaiue oeeo
ooieoe?e /a?ac a?aie/i? cia/aiiy aiae?oe/ieo ooieoe?e; ?ica’ycaiiy ?yaeo
e?aeiaeo caaea/ aeey ??cieo oei?a iaeanoae c iaoith aeyaeaiiy iaaieo
caeiiii??iinoae, ui iathoue i?noea i?e canoinoaaii? aeuaiacaaii?
iaoiaeeee; canoinoaaiiy ?ic?iaeaii? iaoiaeeee aei ?ica’ycaiiy
i?inoi?iaeo a?naneiao?e/ieo caaea/ iaoai?ee a’ycei? ianoeneeai? ??aeeie.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Ia iniia? aeine?aeaeaiiy
aia?aoieo oa ye?nieo aeanoeainoae iniiaiiai ?ioaa?aeueiiai cia?aaeaiiy
ok-aiae?oe/ieo ooieoe?e a aeena?oaoe?ei?e ?iaio? aia?oa
iaea?aeaii aea?aaeaioi? eiio ?ioaa?aeuei? cia?aaeaiiy ok-aiae?oe/ieo
ooieoe?e /a?ac a?aie/i? cia/aiiy aiae?oe/ieo ooieoe?e. ?ic?iaeaii iiao
aoaeoeaio iaoiaeeeo ?ica’ycaiiy e?aeiaeo caaea/ aeey ae?ioe/ieo nenoai
aeeoa?aioe?aeueieo ??aiyiue ia iniia? iaoiaeo
p-aiae?oe/ieo ooieoe?e (p=ok, k=const>0), yea aaco?oueny ia aeei?enoaii?
aeacaieo aeua ?ioaa?aeueieo cia?aaeaiue oeeo ooieoe?e /a?ac a?aie/i?
cia/aiiy aiae?oe/ieo ooieoe?e. Aiia oa?aeoa?eco?oueny oaeeie iiiaioaie:

1) ?ica’ycaiiy e?aeiaeo caaea/ ok-aiae?oe/ieo ooieoe?e ia aeiaaa?
?ica’ycaiiy e?aeiaeo caaea/ aiae?oe/ieo ooieoe?e, a caiaeeoueny i?inoi
aei aecia/aiiy a?aie/ieo cia/aiue aiae?oe/ieo ooieoe?e;

2) iiaeia i?iaiaeeoe ye?ni? aeine?aeaeaiiy iaea?aeaieo ?ica’yce?a a
ie?aieo oi/eao ?, ioaea, ae?noaaaoe ?ica’ycie caaea/ c iaia?aae
caaeaiith iiaaae?ieith a ie?aieo oi/eao a?aieoe? iaeano?, oiaoi a ??cieo
eeanao ooieoe?e; ?nio? iiaeeea?noue aeineoue i?inoi aeine?aeaeoaaoe
ieoaiiy ?nioaaiiy oa ?aeeiino? ?ica’yce?a e?aeiaeo caaea/;

3) iaoiaeeea aoaeoeaii canoiniaaia, cie?aia, i?e ?ica’ycaii? e?aeiaeo
caaea/ aeey iaeanoae: i?ae?oa, i?aaa i?aieiueia c aeeeiooei i?ae?oaii,
i?aaa i?aieiueia c ?ic??cii ii aeoc? eiea;

4) ?ica’ycee e?aeiaeo caaea/, ye? io?eiothoueny ca aeiiiiiaith oe???
iaoiaeeee, aeineoue i?inoi ?aae?cothoueny ia AII;

5) iaoaiaoe/i? ?aea?, ye? aeei?enoiaothoueny a oe?e iaoiaeeoe? i?e
?ica’ycaii? e?aeiaeo caaea/ ok-aiae?oe/ieo ooieoe?e, iiaeooue aooe
aeei?enoaii? e i?e ?ica’ycaii? e?aeiaeo caaea/ aeey ?ioeo eean?a
?-aiae?oe/ieo ooieoe?e.

?ic?iaeaia iaoiaeeea canoiniaaia aei ?ica’ycaiiy i?inoi?iai?
a?naneiao?e/ii? caaea/? iaoai?ee a’ycei? ianoeneeai? ??aeeie – caaea/?
i?i iao?eaiiy a?naneiao?e/iei iioieii a’ycei? ianoeneeai? ??aeeie
noa?e/iiai aeenea, ui iaa?oa?oueny iaaeiei a?n? neiao??? c iaaiith
eooiaith oaeaee?noth.

Aeinoia??i?noue io?eiaieo a ?iaio? ?acoeueoao?a caaacia/o?oueny no?iaith
iinoaiiaeith e?aeiaeo caaea/, canoinoaaiiyi aeey ?o ?ica’ycaiiy
oai?aoe/ii iaa?oioiaaieo oi/ieo iaoiae?a, ii??aiyiiyi a ie?aieo
aeiaaeeao c ?acoeueoaoaie ?ioeo aaoi??a.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Aeena?oaoe?eia ?iaioa ia?
oai?aoe/iee oa?aeoa? ? ? aeeaaeii a ia?niaeoeaiee iai?yiie
aeine?aeaeaiue e?aeiaeo caaea/ aeey ae?ioe/ieo nenoai aeeoa?aioe?aeueieo
??aiyiue, caniiaaiiio ia ?icaeoeo iaoiae?a ocaaaeueiaieo aiae?oe/ieo
ooieoe?e. Io?eiai? a aeena?oaoe?? ?acoeueoaoe noiniaii ?ioaa?aeueieo
cia?aaeaiue oa iaoiaeeee ?ica’ycaiiy e?aeiaeo caaea/ ?-aiae?oe/ieo
ooieoe?e (p=ok, k=const>0), oiaoi e?aeiaeo caaea/ aeey ae?ioe/ieo nenoai
aeeoa?aioe?aeueieo ??aiyiue, iiaeooue aooe aeei?enoai? i?e
aeine?aeaeaii? oa ?ica’ycaii? oe?ieiai eeano caaea/ iaoaiaoe/ii? o?ceee,
iaoai?ee nooe?eueieo na?aaeiaeu, ui caiaeyoueny aei e?aeiaeo caaea/ aeey
aeuaiacaaieo nenoai ??aiyiue. Oi/i? ?ica’ycee, io?eiai? i?e ?ica’ycaii?
e?aeiaeo caaea/ aeey ae?ioe/ieo nenoai aeeoa?aioe?aeueieo ??aiyiue ia
iniia? iaoiaeo ?-aiae?oe/ieo ooieoe?e (p=ok, k=const>0) aeey iaeanoae:
i?ae?oa, i?aaa i?aeiueia c aeeeiooei i?ae?oaii, i?aaa i?aieiueia c
?ic??cii, iiaeooue aooe aeei?enoai?, cie?aia, ye oanoia? aeey ioe?iee
yeino? iaaeeaeaieo iaoiae?a. ?acoeueoaoe, iaea?aeai? i?e ?ica’ycaii?
i?inoi?iai? a?naneiao?e/ii? caaea/? iaoai?ee a’ycei? ianoeneeai? ??aeeie
– caaea/? i?i iao?eaiiy noa?e/iiai aeenea, ui iaa?oa?oueny, iiaeooue
aooe aeei?enoai? oaeiae i?e aeine?aeaeaii? ?ooo aeaoi?iiaaieo e?ia’yieo
o?eaoeue a o?c?ieia??, o?i?/i?e oaoiieia??.

Iniaenoee aianie caeiaoaa/a. An? iaoeia? ?acoeueoaoe, aeeth/ai? a
aeena?oaoe?eio ?iaioo, iaea?aeaii caeiaoaa/ai naiino?eii. A ?iaioao,
iaienaieo o ni?aaaoi?noa? c I.I.Eaioeaei, iinoaiiaee caaea/ oa iaoeiaa
ea??aieoeoai iaeaaeaoue aeieoi?o o?ceei-iaoaiaoe/ieo iaoe, i?ioani?o
I.I.Eaioeaiio, a iaea?aeaiiy eiie?aoieo ?acoeueoao?a oa ?o
aeine?aeaeaiiy aeeiiaii iniaenoi aeena?oaioeith.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe, aeeeaaeai? a aeena?oaoe??,
aeiiia?aeaeeny oa iaaiai?thaaeeny ia ?anioae?eainuee?e
iaoeiai-iaoiaee/i?e eiioa?aioe??, i?enay/aiee 200-??//th c aeiy
ia?iaeaeaiiy Eiaa/aanueeiai (Iaeana, 1992 ?.), ia VI I?aeia?iaei?e
Iaoeia?e eiioa?aioe?? ?i. aeaae. I. E?aa/oea (Ee?a, 1997 ?.), ia
nai?ia?ao eaoaae?e iaoaiaoe/ii? o?ceee Ee?anueeiai oi?aa?neoaoo
?iai? Oa?ana Oaa/aiea, ia i?aeaoc?anueeiio nai?ia?? “Aeeoa?aioe?aeuei?
??aiyiiy oa ?o canoinoaaiiy” a Iaoe?iiaeueiiio oaoi?/iiio oi?aa?neoao?
Oe?a?ie (Ee?a, 1997 ?.), ia nai?ia?? a?aeae?eo iaoaiaoe/ii? o?ceee ?
oai??? iae?i?eieo eieeaaiue ?inoeoooo iaoaiaoeee IAI Oe?a?ie (Ee?a, 1998
?.).

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a 7 iaoeiaeo
i?aoeyo, c yeeo 4 iaienaii aac ni?aaaoi??a, a 5 iaae?oeiaaii o
aeaeaiiyo, ui aoiaeyoue o ia?ae?e iaoeiaeo aeaeaiue, caoaa?aeaeaieo AAE
Oe?a?ie.

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio,
o?ueio ?icae?e?a, aeniiae?a, nieneo aeei?enoaieo aeaea?ae (109
iaeiaioaaiue). Caaaeueiee ianya aeena?oaoe?? noaiiaeoue 129 noi??iie,
iniiaiee oaeno ?iaioe (a o. /. 9 ?enoie?a) aeeeaaeaii ia 116 noi??ieao.

Aeine?aeaeai? a aeena?oaoe?? caaea/? aoee iinoaaeai? ia?oei iaoeiaei
ea??aieeii Ieaen??i Ieaen?eiae/ai Eaioeaei. Aaoi? c aeeaieith
aaey/i?noth caaaeo? ni?ai?aoeth c iei. Aaoi? oaeiae aeneiaeth? ue?o
iiaeyeo ae?oaiio iaoeiaiio ea??aieeia? Aiae??th A?naiiae/o Aeouaieo ca
iino?eio oaaao aei ?iaioe oa i?aeo?eieo ia caaa?oaeueiiio ?? aoai?.

INIIAIEE CI?NO

O anooi? iaa?oioiaaii aeooaeuei?noue oaie oa aeioe?euei?noue ?iaioe,
iaaaaeaii iaeyae aeine?aeaeaiue a iaeano? e?aeiaeo caaea/ ocaaaeueiaieo
aiae?oe/ieo ooieoe?e ?, cie?aia, ?-aiae?oe/ieo ooieoe?e, aeacaii iaoo
?iaioe, iaoeiao iiaecio oa i?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a
aeena?oaoe??, noenei aeeeaaeaii ci?no ?iaioe ca ?icae?eaie.

A ia?oiio ?icae?e? iaaaaeaii iniiai? ?acoeueoaoe A.I. Iieiae?y ii
aea/aiith iniiaiiai ?ioaa?aeueiiai cia?aaeaiiy p-aiae?oe/ieo ooieoe?e c
oa?aeoa?enoeeith p=ok (k=const>0) oa oi?ioe eiai iaa?iaiiy, a oaeiae
?acoeueoaoe ye?nieo aeine?aeaeaiue iiaaae?iee ok-aiae?oe/ieo ooieoe?e,
aecia/aieo iniiaiei ?ioaa?aeueiei cia?aaeaiiyi, a ie?aieo oi/eao
a?aieoe? iaeano?, aea i?ae?ioaa?aeueia ooieoe?y ia? iniaeea?noue
noaiaiaaiai oa?aeoa?o. Aeeeaaeaii iia? ?acoeueoaoe: ?ioaa?aeuei?
cia?aaeaiiy p-aiae?oe/ieo ooieoe?e (p=ok, k=const>0) /a?ac a?aie/i?
cia/aiiy aiae?oe/ieo ooieoe?e aeey aeia?eueiiai k=const>0 a ne?i/aii?e
iaeano?, a iane?i/aii?e iaeano? ? aeey oe?eiai iaia?iiai k>0 a iaeano? c
?ic??cii. Noi?ioeueiaaii oa aeiaaaeaii oai?aie, a oaeiae iaea?aeaii
?yae iane?aee?a c oeeo oai?ai, a yeeo ?icaeyiooi oai?aoe/i? ieoaiiy
uiaei iiaeo ?ioaa?aeueieo cia?aaeaiue.

, aea P – iia?aoi?, aecia/aiee iniiaiei ?ioaa?aeueiei cia?aaeaiiyi
xk-aiae?oe/ieo ooieoe?e c ii/aoeiaith oi/eith eiioo?a ?ioaa?oaaiiy ia
a?ae??ceo L. Oiae?

a iaeano? G ia? i?noea cia?aaeaiiy

(1)

,

, a ?iaeaen “+” iicia/a? a?aie/ia cia/aiiy i?e i?aeoiae? aei eiioo?a N;

a iaeano? G ia? i?noea cia?aaeaiiy

(2)

,

;

i?e i?aeoiae? aei eiioo?a N iathoue i?noea cia?aaeaiiy

, (3)

, (4)

.

ooieoe?y, yea ?aaoey?ia ia iane?i/aiiino?, ia? ioeue ia ieae/a k-ai
ii?yaeeo oa caaeiaieueiy? oiiao

. (5)

Oiae?

a iaeaco? G a??ia cia?aaeaiiy

, (6)

i?e i?aeoiae? aei eiioo?a N; D – ae?enia noaea, yea aecia/a?oueny
??ai?noth

; (7)

a iaeano? G ni?aaaaeeeaa cia?aaeaiiy

(8)

; i?e oeueiio

; (9)

a iaeano? G a??ia cia?aaeaiiy

, (10)

, iiaeiai ia?aoeiaoe oyaio a?nue aeua oi/ee b); i?e oeueiio

. (11)

i?e i?aeoiae? aei eiioo?a N iathoue i?noea cia?aaeaiiy

a) k – oe?ea iaia?ia /enei

, (12)

, (13)

, a ae?enia noaea D aecia/a?oueny ??ai?noth (7);

a) k – iaoe?ea /enei — cia?aaeaiiy (12) oa

(14)

,

;

a) k – oe?ea ia?ia /enei — cia?aaeaiiy (12) oa

, (15)

. Oiae?

a iaeano? G ni?aaaaeeeaa cia?aaeaiiy

, (16)

?iaeaene “+” ? “–” iicia/athoue a?aie/i? cia/aiiy i?e i?aeoiae? aei
eiioo?a N ce?aa oa ni?aaa;

2) ia? i?noea ?ioaa?aeueia cia?aaeaiiy

(17)

oaeiaae N

, (18)

a cia?aaeaiiyo (16), (17) aecia/a?oueny ??ai?noth

. (19)

A ae?oaiio ?icae?e? ?ic?iaeaii iiao aoaeoeaio iaoiaeeeo ?ica’ycaiiy
e?aeiaeo caaea/ aeey ae?ioe/ieo nenoai aeeoa?aioe?aeueieo ??aiyiue ia
iniia? iaoiaeo p-aiae?oe/ieo ooieoe?e (p=ok, k=const>0), yea aaco?oueny
ia aeei?enoaii? iiaoaeiaaieo a ia?oiio ?icae?e? ?ioaa?aeueieo
cia?aaeaiue oeeo ooieoe?e /a?ac a?aie/i? cia/aiiy a?aeiia?aeieo
aiae?oe/ieo ooieoe?e.

, a?aeiia?aeii aei aecia/aiiy, aaaaeaiiai A.I.Iieiae??i,
caaeiaieueiythoue ae?ioe/i?e nenoai? aeeoa?aioe?aeueieo ??aiyiue c
/anoeiieie iio?aeieie

(20)

E?aeia? caaea/? aeey ae?ioe/ieo nenoai aeeoa?aioe?aeueieo ??aiyiue
aeaeyaeo (20) i?e p=ok (k=const>0) aea?aaeaioi? e?aeiaei caaea/ai
p-aiae?oe/ieo ooieoe?e c oa?aeoa?enoeeith p=ok (k=const>0).

, yea iaia?a?aii i?iaeiaaeo?oueny ia a?aieoeth iaeano? e caaeiaieueiy?
e?aeia? oiiae

(21)

(22)

– caaeaia m ?ac iaia?a?aii ae?oa?aioe?eiaaia ooieoe?y.

. ?ica’ycie caaea/? ciaeaeaii o aeaeyae?

(23)

,

aea

(24)

,

(1((), (2(() – a?aeii? ooieoe??,

, (25)

, oi ?ica’ycie caaea/? caienaii o aeaeyae?

, (26)

aea

, (27)

(1((), (2(() – a?aeii? ooieoe??.

?ica’ycie caaea/? ciaeaeaii o aeaeyae?

, (28)

aea

, (29)

(1(()– a?aeiia ooieoe?y,

Ca aeiiiiiaith ?ic?iaeaii? iaoiaeeee io?eiaii aoaeoeai? ?ica’ycee
e?aeiaeo caaea/ ok-aiae?oe/ieo ooieoe?e aeey iaeanoae:

1) i?ae?oa;

2) i?aaa i?aieiueia c aeeeiooei i?ae?oaii;

3) i?aaa i?aieiueia c ?ic??cii ii aeoc? eiea.

sseui iaoiaeeea ?ica’ycaiiy oeeo caaea/ ca aeiiiiiaith iniiaiiai
?ioaa?aeueiiai cia?aaeaiiy ok-aiae?oe/ieo ooieoe?e aeicaiey? caanoe ?o
?ica’ycaiiy, ye i?aaeei, aei ?ica’ycaiiy caaea/? ??iaia-A?eueaa?oa aeey
aiae?oe/ieo ooieoe?e, oi ?ica’ycie an?o ?icaeyiooeo e?aeiaeo caaea/
ok-aiae?oe/ieo ooieoe?e ca aeiiiiiaith iiai? iaoiaeeee ciaeaeaii
aeiyoeiai i?inoi e caaaeaii aei aecia/aiiy a?aie/iiai cia/aiiy
a?aeiia?aeii? aiae?oe/ii? ooieoe?? (ye oea ia? i?noea o aeiaaeeo caaea/
aeey i?ae?oaa, aeey i?aai? i?aieiueie c aeeeiooei i?ae?oaii) aai aei
aecia/aiiy no?eaea a?aeiia?aeii? aiae?oe/ii? ooieoe?? ocaeiaae ?ic??co
(ye oea ia? i?noea o aeiaaeeo caaea/ aeey i?aai? i?aieiueie c ?ic??cii
ii aeoc? eiea). Aeey an?o o?ueio aeiaaee?a iaeanoae ?icaeyiooi ??ci?
oeie e?aeiaeo oiia, a oiio /ene? e ci?oai? e?aeia? oiiae. Io?eiai?
?ica’ycee e?aeiaeo caaea/ ok-aiae?oe/ieo ooieoe?e i?e k=1 ni?aiaaeathoue
c ?ica’yceaie, iaea?aeaieie ?ai?oa I.I.Eaioeaei.

?ica’ycaiiy ci?oaieo caaea/ ok-aiae?oe/ieo ooieoe?e aeey i?ae?oaa oa
aeey i?aai? i?aieiueie c aeeeiooei i?ae?oaii caaaeaii aei ?ica’ycaiiy
?ioaa?aeueieo ??aiyiue O?aaeaieueia II ?iaeo. Aeacaii eeane ooieoe?e, a
yeeo ?ica’ycee oeeo ?ioaa?aeueieo ??aiyiue ?niothoue ? ?aeei?.

?ica’ycee ?aooe caaea/ iaea?aeaii a yaiiio aeaeyae?. I?iaaaeaii
aeine?aeaeaiiy iiaaae?iee iaea?aeaieo ?ica’yce?a i?e i?aeoiae? aei
ie?aieo oi/ie a?aieoe? iaeano?, aei e?ioeaaeo oi/ie ?ic??co.

c oa?aeoa?enoeeith p=x3 a iaeano? G ia?eae?aiiiai ia?a??co iioieo, yea
caaeiaieueiy? e?aeia? oiiae

(30)

(-(/2((((; (0) /a?ac a?aie/i? cia/aiiy aiae?oe/ieo ooieoe?e aeey
aeayeeo ne?i/aiieo oa iane?i/aiieo iaeanoae

2. ?ic?iaeaii iiao aoaeoeaio iaoiaeeeo ?ica’ycaiiy e?aeiaeo caaea/ aeey
ae?ioe/ieo nenoai aeeoa?aioe?aeueieo ??aiyiue ia iniia? iaoiaeo
p-aiae?oe/ieo ooieoe?e (p=ok, k=const>0), yea aaco?oueny ia aeei?enoaii?
iiaoaeiaaieo ?ioaa?aeueieo cia?aaeaiue oeeo ooieoe?e /a?ac a?aie/i?
cia/aiiy a?aeiia?aeieo aiae?oe/ieo ooieoe?e. Ca aeiiiiiaith ?ic?iaeaii?
iaoiaeeee io?eiaii aoaeoeai? ?ica’ycee e?aeiaeo caaea/ ok-aiae?oe/ieo
ooieoe?e aeey iaeanoae:

1) i?ae?oa;

2) i?aaa i?aieiueia c aeeeiooei i?ae?oaii;

3) i?aaa i?aieiueia c ?ic??cii ii aeoc? eiea.

?ica’ycaiiy ci?oaieo caaea/ ok-aiae?oe/ieo ooieoe?e aeey i?ae?oaa oa
aeey i?aai? i?aieiueie c aeeeiooei i?ae?oaii caaaeaii aei ?ica’ycaiiy
?ioaa?aeueieo ??aiyiue O?aaeaieueia II ?iaeo. Aeacaii eeane ooieoe?e, a
yeeo ?ica’ycee oeeo ?ioaa?aeueieo ??aiyiue ?niothoue ? ?aeei?.

?ica’ycee ?aooe aeacaieo aeua caaea/ iaea?aeaii a yaiiio aeaeyae?.
I?iaaaeaii aeine?aeaeaiiy iiaaae?iee iaea?aeaieo ?ica’yce?a i?e
i?aeoiae? aei ie?aieo oi/ie a?aieoe? iaeano?. Io?eiai? ?ica’ycee
e?aeiaeo caaea/ ok-aiae?oe/ieo ooieoe?e i?e k=1 ni?aiaaeathoue c
?ica’yceaie, iaea?aeaieie ?ai?oa I.I.Eaioeaei. ?acoeueoaoe, iaea?aeai? a
?iaio?, noiniaii ?ioaa?aeueieo cia?aaeaiue ok-aiae?oe/ieo ooieoe?e /a?ac
a?aie/i? cia/aiiy a?aeiia?aeieo aiae?oe/ieo ooieoe?e oa iaoiaeeee
?ica’ycaiiy e?aeiaeo caaea/ ? ocaaaeueiaiiyi ?acoeueoao?a I.I.
Eaioeaiai, io?eiaieo aeey o-aiae?oe/ieo ooieoe?e.

3. Ia iniia? cai?iiiiiaaii? iaoiaeeee ?ica’ycaii oa aeine?aeaeaii
caaea/o i?i iao?eaiiy a’yceith ianoeneeaith ??aeeiith noa?e/iiai aeenea,
ui iaa?oa?oueny iaaeiei a?n? neiao??? c? noaeith eooiaith oaeaee?noth.
?ica’ycie caaea/? io?eiaii a yaiiio aeaeyae?. A ?acoeueoao? ye?nieo
aeine?aeaeaiue iaea?aeaiiai ?ica’yceo anoaiiaeaii: i?e i?aeoiae? aei
e?ioeaaeo oi/ie ?ic??co eiiiiiaioe oaeaeeino? iaiaaeai?, a eiiiiiaioe
iai?oa i?yiothoue aei iane?i/aiiino? ii?yaeeo 1/2.

Aeey ii??aiyiiy c ?acoeueoaoaie ?ia?o ?ioeo aaoi??a ?icaeyiooi ie?aiee
aeiaaeie, eiee noa?e/iee aeene ooai?aiee iaa?oaiiyi aeoae iaeeie/iiai
eiea.

?acoeueoaoe, io?eiai? a aeena?oaoe?ei?e ?iaio?, na?ae/aoue i?i oa, ui
iaoiae ?-aiae?oe/ieo ooieoe?e, cie?aia, ok-aiae?oe/ieo ooieoe?e ?
aoaeoeaiei iaoiaeii ?ica’ycaiiy oa aeine?aeaeaiiy e?aeiaeo caaea/ aeey
ae?ioe/ieo nenoai aeeoa?aioe?aeueieo ??aiyiue, aeinoaoiuei oe?ieiai
eeano caaea/ iaoaiaoe/ii? o?ceee, iaoai?ee, ye? caiaeyoueny aei e?aeiaeo
caaea/ ok-aiae?oe/ieo ooieoe?e. Aiie noaaeyoue eiai a iaeei ?yae c
?ioeie a?aeiieie no/anieie aiae?oe/ieie iaoiaeaie oai??? ae?ioe/ieo
nenoai aeeoa?aioe?aeueieo ??aiyiue.

?acoeueoaoe aeena?oaoe?? iiaeooue ciaeoe canoinoaaiiy i?e ?ica’ycaii?
eiie?aoieo i?eeeaaeieo caaea/ iaoaiaoe/ii? o?ceee, iaoai?ee nooe?eueieo
na?aaeiaeu, oai??? iioaioe?aeo, oai??? o?eueo?aoe??, aeaeo?inoaoeee,
iaai?oinoaoeee, ye? caiaeyoueny aei e?aeiaeo caaea/ ?-aiae?oe/ieo,
cie?aia, ok-aiae?oe/ieo ooieoe?e, oiaoi aei e?aeiaeo caaea/ aeey
ae?ioe/ieo nenoai aeeoa?aioe?aeueieo ??aiyiue. ?acoeueoaoe, iia’ycai? c
e?aeiaeie caaea/aie aeey noa?e/iiai aeenea, iiaeooue aooe aeei?enoai?,
cie?aia, a o?c?ieia?? (?oo aeaoi?iiaaieo /a?aiieo e?ia’yieo o?eaoeue), a
o?i?/i?e oaoiieia?? oiui.

NIENIE IIOAE?EIAAIEO I?AOeUe CA OAIITH AeENA?OAOe??

Eaioeaee I.I., Eeai ?.A. ?ica’ycaiiy e?aeiaeo caaea/ ok–aiae?oe/ieo
ooieoe?e aeey i?ae?oaa // Ia/ene. oa i?eee. iaoaiaoeea.– Ee?a: Eea?aeue,
1992.– Aei. 76.– N. 3–12.

Eaioeaee I.I., Eeai I.A. Iioaa?aeuei? cia?aaeaiiy ok-aiae?oe/ieo
ooieoe?e a iane?i/aii?e iaeano? /a?ac a?aie/i? cia/aiiy aiae?oe/ieo
ooieoe?e // A?niee Ee?anuee. oi-oo. Na?.: o?c.-iao. iaoee.– 1993.– N.
20–28.

Eeai I.A. ?ioaa?aeueia cia?aaeaiiy ok-aiae?oe/ieo ooieoe?e aeey
i?aieiueie c ?ic??cii oa eiai canoinoaaiiy aei ?ica’ycaiiy e?aeiaeo
caaea/ // A?niee Ee?anuee. oi-oo. Na?.: o?c.-iao. iaoee.– 1997.– Aei.
1.– N. 60–68.

Eeai I.A. I?i iaeio e?aeiao caaea/o ok-aiae?oe/ieo ooieoe?e aeey
i?aieiueie c aeeeiooei i?ae?oaii // A?niee Ee?anuee. oi-oo. Na?.:
o?c.-iao. iaoee.– 1997.– Aei. 4.– N. 42–50.

Eeai I.A. Iaoiae ?-aiae?oe/ieo ooieoe?e a iaoai?oe? a’ycei? ianoeneeai?
??aeeie // Aieeinueeee iaoai. a?niee.– 1997– Aei. 4.– N. 63–66.

Klen I.V. Mixed boundary value problem of xk-analytical functions for a
half plane with a section // Oinoa I?aeia?. Iaoeiaa eiio. ?i. aeaae. I.
E?aa/oea (15–17 o?aaiy 1997 ?.). Iaoa??aee eiioa?aioe??.– Ee?a.– 1997.–
N. 196–198.

Eaioeaee I.I., Eeai I.A., Eiiiiin E.I., Noiyi I.I. Iaoiaee ?-aiae?oe/ieo
ooieoe?e a e?aeiaeo caaea/ao iaoaiaoe/ii? o?ceee // ?ani.
iaoeiai-iaoiae. eiio., i?enay/. 200-??//th c aeiy ia?iaeaeaiiy
Eiaa/aanueeiai (3–8 aa?aniy 1992 ?.). Oac. aeii..– Iaeana.– 1992.– *.
2.– N. 18–19.

Eeai ?.A. Iaoiae p-aiae?oe/ieo ooieoe?e a e?aeiaeo caaea/ao aeey
ae?ioe/ieo nenoai aeeoa?aioe?aeueieo ??aiyiue. ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.02 –
aeeoa?aioe?aeuei? ??aiyiiy.– Ee?anueeee oi?aa?neoao ?iai? Oa?ana
Oaa/aiea, Ee?a, 1999.

Aeena?oaoe?th i?enay/aii ?ic?iaoe? iiaeo aoaeoeaieo iaoiae?a ?ica’ycaiiy
e?aeiaeo caaea/ aeey iaeiiai eeano ae?ioe/ieo nenoai aeeoa?aioe?aeueieo
??aiyiue c /anoeiieie iio?aeieie ia iniia? iaoiaeo ?-aiae?oe/ieo
ooieoe?e (?=ok, k=const>0). Aia?oa iaea?aeaii ?ioaa?aeuei? cia?aaeaiiy
?-aiae?oe/ieo ooieoe?e (?=ok, k=const>0) /a?ac a?aie/i? cia/aiiy
aiae?oe/ieo ooieoe?e aeey aeayeeo ne?i/aiieo oa iane?i/aiieo iaeanoae.
Ia iniia? oeeo ?ioaa?aeueieo cia?aaeaiue ?ic?iaeaii iiao aoaeoeaio
iaoiaeeeo ?ica’ycaiiy e?aeiaeo caaea/ ?-aiae?oe/ieo ooieoe?e (?=ok,
k=const>0) aeey iaeanoae: i?ae?oa, i?aaa i?aieiueia c aeeeiooei
i?ae?oaii, i?aaa i?aieiueia c ?ic??cii. Aeey an?o o?ueio iaeanoae
?icaeyiooi ??ci? oeie e?aeiaeo oiia. ?ic?iaeaia iaoiaeeea canoiniaaia
aei ?ica’ycaiiy i?inoi?iai? a?naneiao?e/ii? caaea/? iao?eaiiy a’yceith
??aeeiith noa?e/iiai aeenea, ui iaa?oa?oueny.

Eeth/ia? neiaa: ae?ioe/ia nenoaia aeeoa?aioe?aeueieo ??aiyiue,
ocaaaeueiaia aiae?oe/ia ooieoe?y, e?aeiaa caaea/a, ?ioaa?aeueia
cia?aaeaiiy, a?aie/ia cia/aiiy.

Eeai E.A. Iaoiae p-aiaeeoe/aneeo ooieoeee a e?aaauo caaea/ao aeey
yeeeioe/aneeo nenoai aeeooa?aioeeaeueiuo o?aaiaiee. ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.02 –
aeeooa?aioeeaeueiua o?aaiaiey.– Eeaaneee oieaa?neoao eiaie Oa?ana
Oaa/aiei, Eeaa, 1999.

Aeenna?oaoeey iinayuaia ?ac?aaioea iiauo yooaeoeaiuo iaoiaeia ?aoaiey
e?aaauo caaea/ aeey iaeiiai eeanna yeeeioe/aneeo nenoai
aeeooa?aioeeaeueiuo o?aaiaiee a /anoiuo i?iecaiaeiuo ia iniiaa iaoiaea
?-aiaeeoe/aneeo ooieoeee (?=ok, k=const>0). Aia?aua iieo/aiu
yeaeaaeaioiua iniiaiiio eioaa?aeueiiio i?aaenoaaeaieth p-aiaeeoe/aneeo
ooieoeee n oa?aeoa?enoeeie ?=ok, onoaiiaeaiiiio A.I.Iieiaeei,
eioaa?aeueiua i?aaenoaaeaiey p-aiaeeoe/aneeo ooieoeee (?=ok, k=const>0)
/a?ac a?aie/iua cia/aiey aiaeeoe/aneeo ooieoeee aeey iaeioi?uo eiia/iuo
e aaneiia/iuo iaeanoae. Ia iniiaa yoeo eioaa?aeueiuo i?aaenoaaeaiee
?ac?aaioaia iiaay yooaeoeaiay iaoiaeeea ?aoaiey e?aaauo caaea/
p-aiaeeoe/aneeo ooieoeee (?=ok, k=const>0) aeey iaeanoae: iieoe?oa,
i?aaay iieoieineinoue n aua?ioaiiui iieoe?oaii, i?aaa iieoieineinoue n
?ac?acii ii aeoaa ie?oaeiinoe. Aeey anao o?ao iaeanoae ?anniio?aiu
?acee/iua oeiu e?aaauo oneiaee. ?aoaiea e?aaauo caaea/ n iiiiuueth iiaie
iaoiaeeee ia o?aaoao ?aoaiey e?aaaie caaea/e ?eiaia-Aeeueaa?oa aeey
aiaeeoe/aneeo ooieoeee, a iaoiaeeony eneeth/eoaeueii i?inoi e naiaeeony
oieueei e ii?aaeaeaieth a?aie/iiai cia/aiey niioaaonoaothuae
aiaeeoe/aneie ooieoeee (a neo/aa caaea/ aeey iieoe?oaa e aeey i?aaie
iieoieineinoe n aua?ioaiiui iieoe?oaii) eee e ii?aaeaeaieth nea/ea
niioaaonoaothuae aiaeeoe/aneie ooieoeee aaeieue ?ac?aca (a neo/aa caaea/
aeey iieoieineinoe n ?ac?acii ii aeoaa ie?oaeiinoe). ?aoaiea niaoaiiuo
caaea/ aeey iieoe?oaa e aeey i?aaie iieoieineinoe n aua?ioaiiui
iieoe?oaii naaaeaii e ?aoaieth eioaa?aeueiuo o?aaiaiee O?aaeaieueia
aoi?iai ?iaea. ?aoaiea inoaeueiuo caaea/ iieo/aii a yaiii aeaea.
?ac?aaioaiiay iaoiaeeea i?eiaiaia e ?aoaieth i?ino?ainoaaiiie
inaneiiao?e/iie caaea/e iaoaeaiey ayceie aeeaeeinoueth a?auathuaainy
noa?e/aneiai aeenea. ?aoaiea caaea/e naaaeaii e iaoiaeaeaieth
p-aiaeeoe/aneie ooieoeee n oa?aeoa?enoeeie ?=o3, iienuaathuae
a?auaoaeueiua aeaeaeaiey aeeaeeinoe, e aeaoo p-aiaeeoe/aneeo ooieoeee n
oa?aeoa?enoeeie ?=o, iienuaathueo aeaeaeaiea aeeaeeinoe a iaeanoe
ia?eaeeaiiiai na/aiey iioiea. ?aoaiea caaea/e iieo/aii a yaiii aeaea.
Eae /anoiue neo/ae ?anniio?ai noa?e/aneee aeene, ia?aciaaiiue a?auaieai
aeoae aaeeie/iiai e?oaa z=ei( (–(/2(((0). Iieo/aiu
oi?ioeu aeey eiiiiiaio aaeoi?a nei?inoe e aeaaeaiey, oa?aeoa?ecothueo
iiaaaeaiea oa/aiey i?e iaoaeaiee a?auathuaainy noa?e/aneiai aeenea.

Eeth/aaua neiaa: yeeeioe/aneay nenoaia aeeooa?aioeeaeueiuo o?aaiaiee,
iaiauaiiay aiaeeoe/aneay ooieoeey, e?aaaay caaea/a, eioaa?aeueiia
i?aaenoaaeaiea, a?aie/iia cia/aiea.

Klen I.V. The method of p-analytic functions in boundary value problems
for elliptic systems of differential equations. – Manuscript.

Thesis for the degree of candidate of physical and mathematical
sciences, speciality 01.01.02 – differential equations. – Taras
Shevchenko Kyiv University, Kyiv, 1999.

The thesis is devoted to elaboration of constructive efficient tools for
solving of boundary value problems for one a class of elliptic systems
of partial differential equations based on the method of p-analytic
functions (?=ok, k=const>0). For the first time the integral
representations of p-analytic functions (?=ok, k=const>0) via boundary
values of analytic functions for some finite and infinite domains has
been obtained. A new efficient technique for solving of boundary value
problems of p-analytic functions (?=ok , k=const>0) in such
domains as semi-circle, the right half-plane without the semi-circle,
the right half-plane with a section, has been elaborated on the basis of
these representations. Different types of boundary conditions were
examined for all these three domain. The elaborated technique was
applied to solving of the spatial axisymmetric problem of the flow of a
rotating spherical disk by viscous fluid.

Key words: elliptic system of differential equations, generalized
analytic function, boundary value problem, integral representation,
boundary value.

PAGE 17

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