Деякі задачі теорії усереднення сингулярно збурених диференціальних рівнянь: Автореф. дис… канд. фіз.-мат. наук / Обайд Фоайд Собхі Алі, НАН України

IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?inoeooo iaoaiaoeee

Oiaeae Niaoi Aei Oaaeae

OAeE 517.9

Aeaye? caaea/? oai???

ona?aaeiaiiy neiaoey?ii cao?aieo aeeoa?aioe?aeueieo ??aiyiue

01.01.02 — aeeoa?aioe?aeuei? ??aiyiiy

A a o i ? a o a ? a o

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a — 1998

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia o a?aeae?e? iae?i?eiiai aiae?co Iinoeoooo iaoaiaoeee
Iaoe?iiaeueii? aeaaeaii? iaoe Oe?a?ie.

Iaoeiaee ea??aiee: eaiaeeaeao o?c.-iao. iaoe

NOE?AOIEE Aaneeue Iaaiiae/,

o/aiee nae?aoa? ?I IAI Oe?a?ie.

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

NAIIEEAIEI Aaea??e A?eai?iae/,

Ee?anueeee iaoe?iiaeueiee oi?aa?neoao ?i. Oa?ana

Oaa/aiea, eaoaae?a iaoaiaoe/ii?
o?ceee,

caa?aeoth/ee eaoaae?ith;

eaiaeeaeao o?c.-iao. iaoe

IAEEOAA Aeieo?i A?oae?eiae/,

?inoeooo iaoaiaoeee IAI Oe?a?ie, a?aeae?e

iaoaiaoe/ieo iaoiae?a a
noaoenoe/i?e iaoai?oe?,

iaoeiaee ni?a?ia?oiee

I?ia?aeia onoaiiaa: ?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee

IAI Oe?a?ie, i. Aeiiaoeuee

aiaeei?

ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee D.26.206.02 i?e ?inoeooo?
iaoaiaoeee IAI Oe?a?ie ca aae?anith:

252601 Ee?a 4, INI, aoe, Oa?auaie?anueea 3.

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? ?inoeoooo iaoaiaoeee
IAI Oe?a?ie.

Aaoi?aoa?ao ?ic?neaii “ _30 ” ___aeiaoiy____1998 ?.

O/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee

aeieoi? o?c.-iao. iaoe
A.TH.Eo/ea

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. A o?ceoe?, o?i??, a?ieia??, oaoi?oe? /anoi
aeine?ae-aeothoueny i?ioeane a neeueii iaiaeii??aeieo na?aaeiaeuao, ye?,
ye i?aaeei, iienothoueny aeeoa?aioe?aeueieie ??aiyiiyie c
oaeaeeiinoeeethth/eie eiao?oe??ioaie ? i?eaiaeyoue aei iaiao?aeiino?
iiaoaeiae ona?aaeiaieo iiaeaeae aeey oeeo na?aaeiaeu. Aeineoue /anoi oe?
??aiyiiy i?noyoue ua ? neiaoey?i? cao?aiiy (i?eeeaaeii iiaea neoaeeoe
ieanoeiea c neeueii iaiaeii??aeiiai iaoa??aeo c iaeith aei?noe?noth ).

A oaeeo caaea/ao iaiao?aeii iiaoaeoaaoe iiaeaeue na?aaeiaeua,
eieaeuei? aeanoeaino? yeiai ??cei ci?iththoueny, ? oiio c?o/i?oa
ia?aeoe a?ae i?e?inei-i?/iiai eiai iieno aei iae?ineii?/iiai, oiaoi
?icaeyaeaoe ona?aaeiai? oa?ae-oa?enoeee oaeiai na?aaeiaeua. Oai??y
ona?aaeiaiiy aeey cae/aeieo aeeoa?ai-oe?aeueieo ??aiyiue a ca’yceo c
caaea/aie iaoai?ee aoea noai?aia I.I.Aiaieth-aiaei,
TH.I.Ieo?iiieuenueeei, A.I.Naiieeaieii oa ?o o/iyie. Nenoaiaoe/ia
aea/aiiy o?ce/ieo caaea/, ui i?eaiaeyoue aei ona?aaeiaiiy ??aiyiue a
/anoei-ieo iio?aeieo, ii/aeiny a 70-? ?iee ? iia’ycaia c ?iaioaie A.Aea
Aeaei?aeae?, N.Niaiueiei, A.Aainonaia, AE.E?iina, A.Iaiai?eieao, I.A.
Ie?eiee, A.A.AEe-eiaa oa ?ioeo aaoi??a.

. C oe??th iaoith, ye ? a oai??? cae/aeieo aeeoa?aioe?aeueieo
??a-iyiue, iiaea aooe aeei?enoaiee iaoiae aeaiianooaaieo ?iceeaae?a.
?icaeoie

oeueiai iaoiaeo aeey ??aiyiue a /anoeiieo iio?aeieo cai?iiiiiaaii a
?iaioao I.N. Aaoaaeiaa. A ?iaioao I.A. Ie?eiee, A.A.?in?oueyia, I.C.
Oaia?aa, A.I.Iaianaiei, A.?.Noe?aoiiai iiaoaeiaai? aneiioioe/i?
?icaeiaiiy ?ica’yce?a e?aeiaeo caaea/ aeey ae?ioe/ieo ??aiyiue c
oaeaeeiinoeeethth/eie eiao?oe??ioaie, ye ae?oaiai oae ? aenieiai
ii?yaeeo, a oaeiae aeey nenoaie oai??? i?oaeiino?, ye? a?aoiaoaaee
iiaaae?ieo ?ica’yce?a iiaeeco a?aieoe?.

I?ioa, ia caaaeath/e ia aaeeeo e?euee?noue ?ia?o c aeaii? oaiaoeee,
aaaaoi ieoaiue eeoathoueny a?aee?eoeie. Oae, noaiiaeoue ?ioa?an
ciaoiaeaeaiiy eiao?oe??io?a a?aie/ieo iie?iii?a a oai?aiao oeio O?aaiaia
— E?iaeaeueioa aeey ae?ioe/ieo ??aiyiue aenieiai ii?yaeeo ye c
iino?eieie oae ? c ci?iieie eiao?oe??ioaie. Aeooaeueiith eeoa?oueny
caaea/a iiaoaeiae aneiioioe/iiai ?icaeiaiiy aeey ?ica’yce?a e?aeiaeo
caaea/ aeey neiaoey?ii cao?aieo ae?ioe/ieo ??aiyiue c
oaeaeeiinoeeethth/eie eiao?oe??ioaie aenieiai ii?yaeeo.

Ia?a?aoiaai? aeua ieoaiiy ? noaee i?aaeiaoii ?icaeyaeo aeena?oaoe??.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa
i?iaiaeeeanue ca?aeii c caaaeueiei ieaiii aeine?aeaeaiue
aeeoa?aioe?aeueieo ??aiyiue a /anoeiieo iio?aeieo ?inoeoooo iaoaiaoeee
IAI Oe?a?ie.

, aeey neiaoey?ii cao?aieo ae?ioe/ieo ??aiyiue c
oaeaeeiinoeeethth/eie eiao?oe??ioaie aenieiai ii?yaeeo.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Iniiai? ?acoeueoaoe, ui
aecia/athoue iaoeiao iiaecio ? aeiinyoueny ia caoeno, oae? :

Aeine?aeaeaii iiaaae?ieo ia iane?i/aiiino? ia??iaee/ieo ii an?o
ci?iieo, e??i iaei???, ?ica’yce?a caaea/? Ae???oea a iai?ai?inoi?? aeey
ae?ioe/iiai ??aiyiiy c ia??iaee/ieie eiao?oe??ioaie aenieiai ii?yaeeo.
Ciaeaeaii eiao?oe??ioe iie?iiio ii iaia??iaee/i?e ci?ii?e, aei yeiai ia
iane?i/aiiino? i?yio? oeae ?ica’ycie.

Aiaeia?/ia caaea/a ?iaeyiooa aeey noie aeaio ae?ioe/ieo iia?aoi??a.
Iieacaii, ui ii?yaeie iie?iiio aecia/a? iia?aoi? iaioiai ii?yaeeo.

?icaeyiooa o?aoy e?aeiaa caaea/a aeey ae?ioe/iiai ??aiyiiy ae?oaiai
ii?yaeeo. Ciaeaeaii noaeo aei yei? i?yio? ?ica’ycie caaea/?.

Iiaoaeiaaii aneiioioe/i? ?icaeiaiiy ?ica’yce?a caaea/? Ae???oea a
iai?ai?inoi?? aeey neiaoey?ii cao?aiiai ae?ioe/iiai ??aiyiiy c
oaeaeeiinoeeethth/eie ia??iaee/ieie eiao?oe??ioaie aenieiai ii?yaeeo.

Iieacaii, ui oea aneiioioe/ia ?icaeiaiiy ia? ??ciee aeaeyae a
caeaae-

iino? a?ae nooiaiy neiaoey?iiai cao?aiiy.

5. Ciaeaeaii ioe?iee iioeaee oeeo aneiioioe/ieo ?icaeiaiue.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoaoia. ?acoeueoaoe,
iaea?aeai? a ?iaio?, iiaeia aeei?enoaoe aeey aeine?aeaeaiiy o?ce/ieo
i?ioean?a,

ye? aeieeathoue a neeueii iaiaeii??aeieo na?aaeiaeuao.

Iniaenoee aianie caeiaoaa/a. Ii oaii aeena?oaoe(( iioaeieiaaii
5 ?iaio. Iaoaiaoe/i? ?acoeueoaoe ?ia?o [ 2 — 4 ] iaea?aeai? aeena?oaioii
naiinoieii. A aeaieo ?iaioao ni?aaaoi?o iaeaaeeoue aea?? iai?yieo
aeine?aeaeaiue oa iaaiai?aiiy oai?aoe/ieo ?acoeueoao?a. ?acoeueoaoe
?aooe ?ia?o io?eiai? aeena?oaioii naiinoieii.

Ai?iaaoeiy ?acoeueoaoia aeena?oaoei(. Iniiaii ?acoeueoaoe
aeena?oaoe?? aeiiiaiaeaeenue oa iaaiai?thaaeenue :

1) ia caniaeaiii naiiia?o ic cae/aeieo aeeoa?aioeiaeueieo ?iaiyiue
aiaeaeieo

cae/aeieo aeeoa?aioeiaeueieo ?iaiyiue Iinoeoooo iaoaiaoeee IAI
Oe?a(ie;

2) ia caniaeaiii naiiia?o c iae?i?eiiai aiae?co Iinoeoooo iaoaiaoeee
IAI

Oe?a?ie;

3) ia iiaeia?iaeiie eiioa?aioei( “Aneiioioe/ii oa yeinii iaoiaee a
oai?i?

iaeiiieieo eieeaaiue” (na?iaiue 1997 ?., i. Ee?a);

4) ia iiaeia?iaeiie eiioa?aioei? “No/anii i?iaeaie iaoaiaoeee“ (20 —
28

/a?aiy 1998 ?., i. *a?iiaoei.).

Ioae?eaoe??. Ii oaii aeena?oaoe?? iioae?eiaaio 5 ?iaio, c ieo 2 ?iaioe
naiiai aaoi?a, 4 ?iaioe iaae?oeiaaii a i?iaiaeieo iaoeiaeo i?ioieueieo
aeaeaiiyo.

No?oeoo?a ? ia’?i ?iaioe. Aeena?oaoe?eia ?iaioa ianyaii 132 iaoeiiieni?
noi??iee neeaaea?oueny ?c anooio, aeaio ?icae?e?a, aeniiaeo oa nieneo
oeeoiaaii? e?oa?aoo?e, ui i?noeoue 62 iaeiaioaaiiy.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiao(oueny aeooeuei?noue oaie, oi?ioeth(oueny iaoa
aeine(aeaeaiiy, aea(oueny ei?ioeee aiae(c no/aniiai noaio i?iaeai, ye(
aea/athoueny a aeena?oaoe(( , ( iaaiaeeoueny aiioaoe(y iaea?aeaieo
?acoeueoao(a .

A ?icae?ei I ?icaeyaeathoueny ia?iiaee/ii ii anio ciiiieo , e?ii
iaeii((, ?ica`ycee caaea/i Aei?ioea a iai?ai?inoi?? aeey ae?ioe/iiai
??aiyiiy c iino?eieie oa ci?iieie eiao?oe??ioaie aenieiai ii?yaeeo.
Iieacaii, ui ia iane?i/aiiino? ?ica`ycie oe??? caaea/? i?yio? aei
aeayeiai iie?iiio ii iaia??iaee/i?e ci?ii?e. Ciaeaeai? eiao?oe??ioe
oeueiai iie?iiio. ?icaeyiooa o?aoy e?aeiaa caaea/a aeey ae?ioe/iiai
??aiyiiy ae?oaiai ii?yaeeo.

A (( 1.1 — 1.3 ?icae?eo I ?icaeyaea?oueny ianooiia e?aeiaa
caaea/a :

, (1)

, (2)

,

, (3)

,

aecia-/a?oueny ??ai?noth

ia? i?noea ioe?iea

, (4)

.

aeeiio?oueny oiiaa ae?ioe/iino? :

,

aeiaeaoi? noae?.

aeey ?ica’yceo ae?ioe/iiai ??aiyiiy (1), ye? aeei?enoiaothoueny i?e
aeine?aeaeaii? aneiioioeee ia iane?i/aiiino? ?ica’yce?a caaea/? (1)-(3)
a (( 1.2 , 1.3 , 1.5.

Iieeaaeaii

.

oae?, ui iathoue i?noea ianooii? ioe?iee:

,

.

A ( 1.2 ?icae?eo I ?icaeyaea?oueny e?aeiaa caaea/a (1)-(3) aeey
ae?ioe/iiai ??aiyiiy aenieiai ii?yaeeo c noaeeie eiao?oe??ioaie.

ia? i?noea ianooiia ioe?iea :

aecia/athoueny oi?ioeaie

,

.

A ( 1.3 ?icae?eo I ?icaeyaea?oueny e?aeiaa caaea/a (1)-(3)
aeey ae?ioe/iiai ??aiyiiy ?c ci?iieie eiao?oe??ioaie aenieiai ii?yaeeo.

, ocaaaeueiai? ?ica’ycee ianooiieo caaea/ :

,

, (5)

,

.

ni?aaaaeeea? ianooii? ioe?iee:

.

Ia? i?noea ianooiia oaa?aeaeaiiy.

?icaeyiaii caaea/o (1)-(3) .Oiae? ?nio? iie?iii

aecia/athoueny oi?ioeaie

,

— ?ica’ycee caaea/? (5).

A ( 1.4 ?icae?eo I ?icaeyaea?oueny caaea/a Ae???oea aeey ae?ioe/iiai
??aiyiiy aenieiai ii?yaeeo ?c ci?iieie eiao?oe??ioaie, ye? i?noyoue
iieiaeo? /eaie (aeiaaeie noie aeaio ae?ioe/ieo iia?aoi??a) .

?iceyiaii ianooiio e?aeiao caaea/o :

,

, (6)

,

,

? caaeiaieueiythoue oiiae (4).

Aecia/eii ianooiio iiiaeeio

,

.

.

,

,

ni?aaaaeeeaa ioe?iea

?iceyiaii ianooiio e?aeiao caaea/o :

,

,

, (7)

.

I?eionoeii, ui aeey i?aaeo /anoei aeeiiothoueny oiiae (4).

Ia? i?noea ianooiia oaa?aeaeaiiy .

caaea/i (7) aeeiio?oueny ia??ai?noue

,

.

A ( 1.5 ?icae?eo I ?icaeyaea?oueny o?aoy e?aeiaa caaea/a aeey
ae?ioe/iiai ??aiyiiy ae?oaiai ii?yaeeo.

A ?icae?e? 2 aeena?oaoe?? ?icaeyaeathoueny e?aeia? caaea/? aeey
neiaoey?ii cao?aieo ae?ioe/ieo aeeoa?aioe?aeueiuo ??aiyiue c
oaeaeeiiinoeeethth/eie eiao?oe??ioaie.

?iceyiaii ianooiio e?aeiao caaea/o :

, (9)

,

(10)

,

,

,

aeeiiaia oiiaa ae?ioe/iino? :

.

.

.

A ( 2.1 ?icae?eo 2 aoaeo?oueny aneiioioe/ia ?icaeiaiiy ?ica’yceo

o aeaeyae?

,

aea

.

— ?ica’ycee ?aeo?aioii? iine?aeiaiino? caaea/

,

a?aeiia?aeathoue iia?aie/iei i?ioa?eai ? ? ?ica’yceaie ?aeo?aioii?
iine?aeiaiino? caaea/

,

,

, aea?ai? oae, uia aeeiioaaeenue ia??aiino?

,

c iaioith aeiaaeeiith ioeueoe-?iaeaena.

? ?ica’yceaie ?aeo?aioii? iine?aeiaiino? caaea/:

,

,

aea

.

Ooo aaaaea?oueny, ui

.

Aeiaaaeaii oaa?aeaeaiiy.

.

Iaoae

.

Aeiaaaeaii ianooiia oaa?aeaeaiiy.

o aeaeyae?

,

aea

? ?ica’yceaie ?aeo?aioii? iine?aeiaiino? caaea/:

,

a?aeiia?aeathoue iia?aie/iei i?ioa?eai ? ? ?ica’yceaie ?aeo?aioii?
iine?aeiaiino? caaea/ :

,

,

,

, aea

,

— ocaaaeueiai? ?ica’ycee caaea/

.

.

, aeieeaa? c oai?aie 5.

Iaoae

.

ni?aaaaeeeaa ioe?iea

,

— ocaaaeueiaiee ?ica’ycie caaea/? (8)-(10) .

?icaeyaea?oueny caaea/a

. (12)

— ?ica’ycie caaea/?

,

,

.

INIIAI? ?ACOEUeOAOE OA AENIIAEE

Aeine?aeaeaii iiaaae?ieo ia iane?i/aiiino? ia??iaee/ieo ii an?o
ci?iieo, e??i iaei???, ?ica’yce?a caaea/? Ae???oea a iai?ai?inoi??
aeey ae?ioe/iiai ??aiyiiy c ia??iaee/ieie eiao?oe??ioaie aenieiai
ii?yaeeo. Ciaeaeaii eiao?oe??ioe iie?iiio ii iaia??iaee/i?e ci?ii?e, aei
yeiai ia iane?i/aiiino? i?yio? oeae ?ica’ycie.

Aiaeia?/ia caaea/a ?iaeyiooa aeey noie aeaio ae?ioe/ieo iia?aoi??a.
Iieacaii, ui ii?yaeie iie?iiio aecia/a? iia?aoi? iaioiai ii?yaeeo.

?icaeyiooa o?aoy e?aeiaa caaea/a aeey ae?ioe/iiai ??aiyiiy ae?oaiai
ii?yaeeo. Ciaeaeaii noaeo, aei yei? i?yio? ?ica’ycie caaea/?.

Iiaoaeiaaii aneiioioe/i? ?icaeiaiiy ?ica’yce?a caaea/? Ae???oea a
iai?ai?inoi?? aeey neiaoey?ii cao?aiiai ae?ioe/iiai ??aiyiiy c
oaeaeeiinoeeethth/eie ia??iaee/ieie eiao?oe??ioaie aenieiai ii?yaeeo.

Iieacaii, ui oea aneiioioe/ia ?icaeiaiiy ia? ??ciee aeaeyae a
caeaaeiino? a?ae nooiaiy neiaoey?iiai cao?aiiy.

Ciaeaeaii ioe?iee iioeaee oeeo aneiioioe/ieo ?icaeiaiue.

Iniiai? iieiaeaiiy aeena?oaoe?? iioae?eiaai? a

ianooiieo ?iaioao :

Oieaae Niaoe Iaaeae. I i?aaeaeueiii iieeiiia aeey ?aoaiey yeeeioe/aneiai
o?aaiaiey /aoaa?oiai ii?yaeea n iinoiyiiuie eiyooeoeeaioaie //
Oe?.iao.aeo?i. — 1998. — 50, ? 3 , c. 437-445.

Oieaae Niaoe Iaaeae, Coe?aoiue A. E. I i?aaeaeueiii iieeiiia aeey
?aoaiey yeeeioe/aneiai o?aaiaiey aunieiai ii?yaeea n iinoiyiiuie
eiyooeoeeaioaie // E?aeiai caaea/i aeey aeeoa?aioeiaeueieo ?iaiyiue :
Ca. iaoe. i?. — Ee?a: Ii-o iaoaiaoeee IAI Oe?a?ie , 1998.- Aei.1 (17) .-
C. 192-207.

Coe?aoiue A. E. Oieaae Niaoe Iaaeae. I iiaaaeaiee ia aaneiia/iinoe
?aoaiee e?aaauo caaea/ aeey yeeeioe/aneeo o?aaiaiee aoi?iai ii?yaeea //
Neiao?ieii oa aiaeioe/ii iaoiaee a iaoaiaoe/iie oiceoei : Ca. iaoe. i?.
/ IAI Oe?a?ie. Ii-o iaoaiaoeee;Paaeeie.:A.A.Iieioii oa ii. — Ee?a , 1998
.- C. 232-242.

4. Coe?aoiue A. E. Oieaae Niaoe Iaaeae . Aneiioioe/aneia ?aceiaeaiea
?aoaiee neiaoey?ii aiciouaiiuo yeeeioe/aneeo aeeooa?aioeaeueiuo
o?aaiaiee // Iaeeiaei(a e?aaa(a caaea/e iaoaiaoe/aneie oeceee e eo
i?eeiaeaiey. Na. iaoe. o?. / IAI Oe?aei(. Ei-o iaoaiaoeee; Paaeeie.: A.
I.Naiieeaiei (ioa. ?aae.) , A. A. Aa?acianeee (ioa. ?aae.) , e ae?. —
Eeaa , 1998. C 210 — 214.

5. Oieaae Niaoe Iaaeae . I i?aaeaeueiii iieeiiia aeey ?aoaiey
yeeeioe/aneiai o?aaiaiey /aoaa?oiai ii?yaeea n iinoiyiiuie
eiyooeoeeaioaie // Aneiioioe/ii oa yeinii iaoiaee a oai?i? iaeiiieieo
eieeaaiue : Iiaeia?. eiio.: O?aoi Aiaiethaianueei /eoaiiy, Ee?a, 18-23
ca?iiy 1997 ?. — Ee?a, Ii-o iaoaiaoeee IAI Oe?a?ie, 1997 ?. — C.
126-127.

OAAEAe Oiaeae Niaoi. Aeaye? caaea/? oai??? ona?aaeiaiiy neiaoey?ii
cao?aieo aeeoa?aioe?aeueieo ??aiyiue — Poeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.02 —
aeeoa?aioeiaeueii ?iaiyiiy. — ?inoeooo iaoaiaoeee IAI Oe?a?ie, Ee?a,
1998.

A aeena?oaoe?? iiaoaeiaaii aneiioioe/ia ?icaeiaiiy ?ica’yce?a
e?aeiaeo ca-aea/ aeey neiaoey?ii cao?aieo ae?ioe/ieo ??aiyiue c
oaeaeeiinoeeethth/eie eia-o?oe??ioaie aenieiai ii?yaeeo. Ciaeaeai?
eiao?oe??ioe a?aie/ieo iie?iii?a a oai-?aiao oeio O?aaiaia-E?iaeaeueioa
aeey ae?ioe/ieo ??aiyiue aenieiai ii?yaeeo.

Eeth/ia? neiaa: iaeee ia?aiao?, oaeaeeiinoeeethth/? eiao?oee?ioe ,
neiaoey?ia cao?aiiy, aneiioioe/ia ?icaeiaiiy, ocaaaeueiai? iiiaioe,
caoooaiiy aia?a??.

OAAEAe Oieaae Niaoe. Iaeioi?ua caaea/e oai?ee on?aaeiaiey
neiaoey?ii aiciouaiiuo aeeooa?aioeeaeueiuo o?aaiaiee . — ?oeiienue.

Aeenna?oaoeey ia nineaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoa-iaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.02 —
aeeooa?aioeeaeueiua o?aaiaiey . — Einoeooo iaoaiaoeee IAI Oe?aeiu, Eeaa,
1998.

A aeena?oaoeee iino?iaii aneiioioe/aneia ?aceiaeaiea ?aoaiee e?aaauo
caaea/ aeey neiaoey?ii aiciouaiiuo yeeeioe/aneeo o?aaiaiee n
auno?iinoeeeee?othueie eiyooeoeeaioaie aunieiai ii?yaeea. Iaeaeaiu
eiyooeoeeaiou i?aaeaeueiuo iieeiiiia a oai?aiao oeia O?aaiaia —
Eeiaeaeaoa aeey yeeeioe/aneeo o?aaiaiee aunieiai ii?yaeea.

Eeth/aaua neiaa: iaeue ia?aiao?, auno?iinoeeeee?othuea eiyooeoeeaio(,
neiaoey?iia aiciouaiea, aneiioioe/aneia ?aceiaeaiea, iaiauaiiua iiiaiou,
caoooaiea yia?aee.

OBAID Fouad Sobhi. Problems in theory of averaging for
differential equations with singular perturbation.

Doctor of thesis, speciality 01.01.02 — mathematical physics.
— Institute of Mathematics, National Academy of Science of Ukraine,
Kyiv, 1998.

In this thesis it is built asymptotic expansion of solutions of
boundary value prob-lems for high order partial differential elliptical
equations with singular perturbation and fast-oscillating coefficients.
In additional, it is found coefficients of the polyno-mials in theorems
type Frahmen — Lendilifa for high order elliptical equations.

Key words : small parameter, fast oscillating coefficients,
singular perturbation, asimptotic expansion , generalized moments ,
damping energy.

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