Асимптотичні зображення розв’язків диференціальних рівнянь n-го порядку з нелінійностями типу Емдена-Фаулера: Автореф. дис… канд. фіз.-мат. наук / О

IAeANUeEEE AeA?AEAAIEE OI?AA?NEOAO

?i.?.?.Ia/i?eiaa

OAAAI?IA Ieaia A’y/aneaa?aia

OAeE 517.925.54

ANEIIOIOE*I? CIA?AAEAIIss ?ICA’ssCE?A

AeEOA?AIOe?AEUeIEO ??AIssIUe n-ai II?ssAeEO

C IAE?I?EIINOssIE OEIO AIAeAIA — OAOEA?A

01.01.02 — aeeoa?aioe?aeuei? ??aiyiiy

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Iaeana — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioo aeeiiaii ia eaoaae?? aeeoa?aioe?aeueieo ??aiyiue

Iaeanueeiai aea?aeaaiiai oi?aa?neoaoo ?i.?.?.Ia/i?eiaa

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

?AOOOIA A’y/aneaa Ieoaeeiae/, Iaeanueeee aea?aeaaiee oi?aa?neoao
?i.?.?.Ia/i?eiaa, caa?aeoaa/ eaoaae?e aeeoa?aioe?aeueieo ??aiyiue.

Io?oe?ei? iiiiaioe: aeaaeai?e AI A?oc??, aeieoi? o?ceei-iaoaiaoe/ieo
iaoe, i?ioani? E?AO?AAeCA ?aai Oa??aeiae/, ?inoeooo iaoaiaoeee
?i.A.?aciaaeca AI A?oc??, aee?aeoi?;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? OAIE?INUeEEE TH??e
Aieiaeeie?iae/, Eai’yiaoeue-Iiae?euenueeee iaaeaaia?/iee oi?aa?neoao,
caa?aeoaa/ eaoaae?e.

I?ia?aeia onoaiiaa: Ee?anueeee iaoe?iiaeueiee oi?aa?neoao ?i.Oa?ana
Oaa/aiea, eaoaae?a ?ioaa?aeueieo ??aiyiue.

Caoeno a?aeaoaeaoueny “1” aeiaoiy 1999?. i 15 aiae. ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee E 41.051.05 Iaeanueeiai aea?aeaaiiai
oi?aa?neoaoo ?i.?.?.Ia/i?eiaa ca aae?anith 270026, i.Iaeana,
aoe.Aeai?yinueea,2, aoae.73.

C aeena?oaoe??th iiaeia iciaeiieoenue o iaoeia? a?ae?ioaoe? Iaeanueeiai
aea?aeaaiiai oi?aa?neoaoo ?i.?.?.Ia/i?eiaa (270026, i.Iaeana,
aoe.I?aia?aaeainueea, 24).

Aaoi?aoa?ao ?ic?neaiee “31” na?iiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
A?othe I.I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. O ca’yceo c no/anieie iio?aaaie i?aeoeee
ana a?eueoiai cia/aiiy iaaoaathoue i?iaeaie aeine?aeaeaiiy iae?i?eieo
iaaaoiiiiieo aeeoa?aioe?aeueieo ??aiyiue. Inoaii?i /anii (aeea.
iiiia?ao?th ?.O.E?ao?aaeca, O.A.*aioo??y ”Aneiioioe/aneea naienoaa
?aoaiee iaaaoiiiiiuo iaueiiaaiiuo aeeooa?aioeeaeueiuo o?aaiaiee”.-I.:
Iaoea, 1990) oai??y oaeeo ??aiyiue nooo?ai iioe?eeany ca ?aooiie cia/ii?
e?eueeino? ?acoeueoao?a i?eioeeiiaiai oa?aeoa?o. Iai?eeeaae, aeaii
eeaneo?eaoe?th ??aiyiue ca inoeeeyoe?eieie aeanoeainoyie ?o ?ica’yce?a,
iaea?aeaii iciaee ?nioaaiiy ? a?aenooiino? neiaoey?ieo, i?aaeeueieo,
eieeaieo, iaeieeaieo oa iiiioiiieo ?ica’yce?a ??cieo oei?a, io?eiaii
aneiioioe/i? ioe?iee aeey aeayeeo oei?a ?ica’yce?a a ieie?
iane?i/aiiino? oa ?i.

Aaeeeo ?ieue a iiaoaeia? aneiioioe/ii? oai??? iae?i?eieo iaaaoiiiiieo
aeeoa?aioe?aeueieo ??aiyiue a?ae?a?aei eeane/ia ??aiyiiy
Aiaeaia-Oaoea?a, ie?ai? aeiaaeee yeiai aeieeathoue a aaaaoueio aaeocyo
i?e?iaeiciaanoaa. Iaea?aeai? aeey oeueiai ??aiyiiy ?acoeueoaoe ni?eyee a
iiaeaeueoiio ?icaeyaeo aeai/eaieo ocaaaeueiaieo ??aiyiue oeio
Aiaeaia-Oaoea?a ae?oaiai ii?yaeeo. A ?iaioao ?.O.E?ao?aaeca,
O.A.*aioo??y, O. Aaeiai?oey, E.A. Eeaaaiiaa, I.A.Eino?ia, A.I. ?aoooiaa
oa ?i. aoee ?ic?iaeai? aoaeoeai? iaoiaee aeine?aeaeaiiy
aneiioioe/iiai iiaiaeaeaiiy an?o ?o i?aaeeueieo oa neiaoey?ieo
?ica’yce?a.

, a oaeiae aneiioioe/i? ioe?iee aeey oae caaieo eiaca?ianueeeo oa
oaeaeeic?inoath/eo ?ica’yce?a.

Ocaaaeueithth/e ?aeath, yeo aoei aeei?enoaii i?e aeine?aeaeaii?
aneiioioe/iiai iiaiaeaeaiiy ?ica’yce?a ??aiyiue oeio
Aiaeaia-Oaoea?a ae?oaiai ii?yaeeo,

I.A. Eino?i cai?iiiioaaa i?aeo?ae canoinoaaiiy oi?ioe A. Oa?ae?

aeey io?eiaiiy aneiioioe/ieo cia?aaeaiue oaeiai oeio eiiieaeniicia/ieo
?ica’yce?a, a?aei?iieo a?ae noaiaiaaeo, iae?i?eieo ??aiyiue n-ai
ii?yaeeo aeaeo

.

— ai ii?yaeeo

,

— ?ica’yce?a.

, yeee caaeiaieueiy? oae? o?e oiiae:

;

;

?nio? ne?i/aiia aai iane?i/aiia a?aieoey

.

(iniaeeaeo) ia ioiieththoueny oi?ioeaie A. Oa?ae?.

O ca’yceo c aeuaaeacaiei aeooaeueiei ? ieoaiiy i?i iioe?aiiy
?acoeueoao?a A.I.?aoooiaa ia ?noioii iae?i?ei? iaaaoiiiii?
aeeoa?aioe?aeuei? ??aiyiiy a?eueo caaaeueiiai aeaeo.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.
Aeena?oaoe?eia ?iaioa aeeiiaia a ?aieao oaie «Aneiioioe/ia iiaaae?iea
?ica’yce?a iaaaoiiiiieo cae/aeieo aeeoa?aioe?aeueieo ??aiyiue», ui
aeeiio?oueny ia eaoaae?? aeeoa?aioe?aeueieo ??aiyiue Iaeanueeiai
aea?aeaaiiai oi?aa?neoaoo ?i.?.?.Ia/ieeiaa ca?aeii c eii?aeeiaoe?eiei
ieaiii iaoeiaeo aeine?aeaeaiue I?i?noa?noaa ina?oe Oe?a?ie c iai?yieo
«Aaiiao?e/i? ? aiae?oe/i? iaoiaee oa ?o canoinoaaiiy».

— ai ii?yaeeo

(1)

— iaia?a?aii aeeoa?aioe?eiaai? ooieoe??,

.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a.

-?ica’yce?a ?noioii iae?i?eieo iaaaoiiiiieo cae/aeieo
aeeoa?aioe?aeueieo ??aiyiue aeaeo (1);

— ?ica’yce?a ??aiyiiy (1);

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?iaioa ia? a
iniiaiiio oai?aoe/iee oa?aeoa?. Aea ?acoeueoaoe aeena?oaoe?? oa
?ic?iaeaia a i?e iaoiaeeea aeine?aeaeaiiy iiaeooue aooe aeei?enoai? aeey
aea/aiiy aneiioioe/ieo aeanoeainoae ?ica’yce?a iae?i?eieo
aeeoa?aioe?aeueieo ??aiyiue n-ai ii?yaeeo a?eueo caaaeueiiai aeaeo, a
oaeiae aeine?aeaeaiiy eiie?aoieo iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue,
ye? o?aieythoueny a oai?aoe/i?e o?ceoe?, iaoai?oe? ? o. ?i.

Iniaenoee aianie caeiaoaa/a. Iai?yiie aeine?aeaeaiue, iinoaiiaea
caaaeaiue oa ?ic?iaea aeayeeo c iaoiae?a aeine?aeaeaiiy iaeaaeaoue
iaoeiaiio ea??aieeia?. ?acoeueoaoe aeena?oaoe??, ye? aeiinyoueny ia
caoeno, iaea?aeai? aaoi?ii naiino?eii.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. ?acoeueoaoe, iaea?aeai? a
aeena?oaoe??, aeiiia?aeaeeny oa iaaiai?thaaeeny ia V
I?aeia?iaei?e iaoeia?e eiioa?aioe?? ?i. aeaaeai?ea I. E?aa/oea (Ee?a,
1996 ?.), ia Anaoe?a?inuee?e eiioa?aioe??
«Aeeoa?aioe?aeueii-ooieoe?iiaeuei? ??aiyiiy oa ?o canoinoaaiiy»
(*a?i?aoe?, 1996?.), ia ? I?aeia?iaei?e iaoeiai-i?aeoe/i?e eiioa?aioe??
«Iaoaiaoeea oa ineoieia?y a iaaeaaia?/i?e nenoai?» (Oaoi?/iee
oi?aa?neoao, Iaeana, 1996 ?.), ia I?aeia?iaei?e iaoeia?e eiioa?aioe??
«Iae?i?ei? e?aeia? caaea/? iaoaiaoe/ii? o?ceee oa ?o canoinoaaiiy»
(Eaiaiaoeue-Iiae?euenueeee, 1996 ?.), ia I?aeia?iaei?e iaoeia?e
eiioa?aioe?? (o?ao? Aiaietha?anuee? /eoaiiy) «Aneiioioe/i? oa ye?ni?
iaoiaee a oai??? iae?i?eieo eieeaaiue» (Ee?a, 1997 ?.), ia iaoeiaeo
nai?ia?ao c ye?nii? oai??? aeeoa?aioe?aeueieo ??aiyiue o
Iineianueeiio aea?aeaaiiio oi?aa?neoao? ?i. Eiiiiiniaa (1997 ?.) ? a
Iaeanueeiio aea?aeaaiiio oi?aa?neoao? ?i ?.?. Ia/ieeiaa.

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a 10
iaoeiaeo ?iaioao. O 5-oe ?iaioao, iaienaieo o ni?aaaoi?noa? c iaoeiaei
ea??aieeii, A.I.?aoooiao iaeaaeaoue iinoaiiaea caaaeaiue oa iai?yiie
aeine?aeaeaiue, a eiie?aoi? ?acoeueoaoe io?eiai? caeiaoaa/ai naiino?eii.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa
neeaaea?oueny c anooio, /ioe?ueio ?icae?e?a, aeniiaeo oa nieneo
oeeoiaaii? e?oa?aoo?e, ui i?noeoue 100 iaeiaioaaiue. Caaaeueiee ianya
?iaioe — 149 noi??iie iaoeiiieniiai oaenoo.

INIIAIEE CI?NO ?IAIOE

O anooi? noenei aena?oeth?oueny noai iaoeiai? i?iaeaie ca oaiith
aeena?oaoe??, iaa?oioiao?oueny aeooaeuei?noue oaie, aea?oueny caaaeueia
oa?aeoa?enoeea ?iaioe ? oi?ioeththoueny iniiai? ?acoeueoaoe, iaea?aeai?
aaoi?ii.

A ia?oiio ?icae?e? aeaii iaeyae e?oa?aoo?e, a yeiio ie?aneaii
iniiai? aoaie ?icaeoeo aneiioioe/ii? oai??? aeeoa?aioe?aeueieo ??aiyiue
c iae?i?eiinoyie oeio Aiaeaia-Oaoea?a ? i?iaiae?ciaaii ?ic?iaeai? aeey
oaeiai oeio ??aiyiue iaoiaee aeine?aeaeaiiy. C aeei?enoaiiyi oeeo
iaoiae?a ? aeiaaaeaieo eai i?i aneiioioeeo ?ica’yce?a iaeiiai eeano
iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue ia?oiai ii?yaeeo ia??oioiaaii
i?aeo?ae aeey aeine?aeaeaiiy iniiaiiai ia’?eoa aeena?oaoe??. Eiio
i?enay/aii ianooii? o?e ?icae?ee ?iaioe. Ooo aeei?enoiaothoueny oae?
aeiiii?aei? iicia/aiiy:

;

;

),

aea

aeeiiothoueny oae? aea? oiiae:

S l.1) ooieoe??

;

a?aieoey

.

J aeeiiothoueny oiiae:

S0.1) ooieoe??

;

a?aieoey

.

.

, i?enay/aii oai?aie 2.1-2.7.

aneiioioe/i? cia?aaeaiiy aeaeo

, (2)

iaeia c cia?aaeaiue:

, (3)

aai

, (4)

,

.

aneiioioe/i? cia?aaeaiiy aeaeo

(5)

iaeia c cia?aaeaiue:

, (6)

aai

, (7)

,

.

A oai?aiao 2.3-2.7 anoaiiaeththoueny iaiao?aei? ? aeinoaoi? oiiae
?nioaaiiy o ??aiyiiy (1) ?ica’yce?a c aneiioioe/ieie cia?aaeaiiyie
(2)-(3); (2),(4); (5)-(6); (5), (7).

aneiioioe/i? cia?aaeaiiy (2)-(3), iaiao?aeii, uia

, (8)

, (9)

. (10)

ii?yae c oiiaaie (8)-(10) aeaaa?a?/ia ??aiyiiy

,

aea

,

— ?ica’ycie aeacaiiai oeio.

aneiioioe/i? cia?aaeaiiy (2), (4) ? a?ae??ciythoueny a?ae ?ica’yce?a
c cia?aaeaiiyie (2), (3), iaiao?aeii, uia aeeiioaaeenue oiiae:

;

;

,

.

ii?yae c oeeie oiiaaie aeaaa?a?/ia ??aiyiiy

,

-?ica’ycie c aneiioioeeaie (2), (4).

aneiioioe/i? cia?aaeaiiy (5), (6), iaiao?aeii, uia aeeiioaaeenue
oiiae

, (11)

, (12)

(13)

(14)

, aeaaa?a?/ia ??aiyiiy

,

aea

,

— ?ica’ycie c aneiioioeeaie (4), (5).

aeeiioaaeenue oiiae:

, .

,

,

.

, i?noyoueny o oai?aiao 3.1-3.6.

aai aneiioioe/i? cia?aaeaiiy aeaeo

(15)

,

aai aneiioioe/i? cia?aaeaiiy

,

(16)

,

,

.

aneiioioe/i? ni?aa?aeiioaiiy:

,

(17 )

.

a?aieoey

.

).

Aeey i?eeeaaeo noi?ioeth?ii aea? c ieo.

? aeey aeayei? o?eniaaii? ia?e

aneiioioe/i? cia?aaeaiiy (15), (17), iaiao?aeii, uia aeeiioaaeenue
oiiae

,

;

,

. sseui ae ii?yae c oeeie oiiaaie

,

-?ica’ycie c aniioioeeaie (15), (17).

aneiioioe/i? cia?aaeaiiy (16) ? a?ae??ciythoueny a?ae ?ica’yce?a c
cia?aaeaiiyie (15), (17), iaiao?aeii ? aeinoaoiuei, uia

,

,

,

.

aeine?aeaeo?oueny o aeiaaeeo ??aiyiiy

. (18)

, a iio?i ae??oo?oueny ieoaiiy (oai?aie 4.2-4.3) i?i oaeoe/ia ?nioaaiiy
o iueiai ?ica’yce?a c iaea?aeaieie aneiioioe/ieie cia?aaeaiiyie.

aai aneiioioe/i? cia?aaeaiiy

J, (19)

aai cia?aaeaiiy aeaeo

, (20)

.

aneiioioe/i? cia?aaeaiiy (19), iaiao?aeii aeeiiaiiy oiia:

, (21)

, (22)

.

A?eueo oiai, yeui ii?yae c oiiaaie (21)-(22) aeaaa?a?/ia ??aiyiiy

,

— ?ica’ycie aeacaiiai oeio.

o aeiaaeeo ia?iiai n ? aeeiioaaeenue oiiae:

, (23)

, (24)

, (25)

.

— ?ica’ycie aeaeo (20).

AENIIAEE

-?ica’yce?a ?noioii iae?i?eieo aeeoa?aioe?aeueiiai ??aiyiiy n-ai
ii?yaeeo aeaeo (1).

-?ica’yce?a ??aiyiiy (1).

-?ica’yce?a c iaea?aeaieie aneiioioe/ieie cia?aaeaiiyie.

.

. Aeaye? c aeiaaee?a ?icaeyiooi i?e neaa?oeo iaiaaeaiiyo ia
aeaaee?noue eiao?oe??io?a ??aiyiiy.

?acoeueoaoe aeena?oaoe?? ? iiaeie ? aeicaieythoue iienaoe aneiioioeeo
ia o?eueee i?aaeeueieo, aea ? neiaoey?ieo ?ica’yce?a ??aiyiiy (1).

NIENIE IIOAE?EIAAIEO I?AOeUe

CA OAIITH AeENA?OAOe??

1. O a a a i ? i a I. A. Ia aneiioioe/aneii iiaaaeaiee ?aoaiee iaeiiai
iaeeiaeiiai aeeooa?aioeeaeueiiai o?aaiaiey n-ai ii?yaeea//Iaeeiaeiua
e?aaaua caaea/e iaoaiaoe/aneie oeceee e eo i?eeiaeaiea. Na.iao/i.o?. IAI
Oe?aeiu.-E., 1996.-N. 275-276.

2. O a a a i ? i a I. A., ? a o o o i a A. I. E aii?ino ia
aneiioioeea ?aoaiee iaeeiaeiuo aeeooa?aioeeaeueiuo o?aaiaiee n-ai
ii?yaeea // Aeeooa?aioeeaeueiua o?aaiaiey.-1997.-o.33, ? 6.- N.858.

O a a a i ? i a I. A. Aneiioioeea ?aoaiee iaeioi?uo iaeeiaeiuo
aeeooa?aioeeaeueiuo o?aaiaiee n-ai ii?yaeea// Aeeooa?aioeeaeueiua e
eioaa?aeueiua o?aaiaiey iaoaiaoe/aneie oeceee e eo i?eeiaeaiey.
Na.iao/i.o?. IAI Oe?aeiu.-E., 1997.-N. 233-236.

S h e b a n i n a E. V., E v t u k h o v V. M. Asymptotic behaviour
of solutions of n-th order differential equations// Mem. Differential
Equations Math. Phys. Tbilisi.-1998.- V.13.-P.150-153.

5. O a a a i e i a A. A. Aneiioioe/aneea i?aaenoaaeaiey
iiiioiiiuo ?aoaiee aeeooa?aioeeaeueiuo o?aaiaiee n -ai ii?yaeea n
iaeeiaeiinoyie oeia Yiaeaia-Oaoea?a //Iaeeiaeiua e?aaaua caaea/e
iaoaiaoe/aneie oeceee e eo i?eeiaeaiey: Na.iao/i.o?. IAI Oe?aeiu.- E.,
1999.-N.270-274.

6. O a a a i ? i a I. A., ? a o o o i a A. I. Ia aneiioioeea
i?aaeeueiuo ?aoaiee iaeioi?uo eeannia iaeeiaeiuo aeeooa?aioeeaeueiuo
o?aaiaiee n-ai ii?yaeea.//Iaoaiaoeea e ineoieiaey a iaaeaaiae/aneie
nenoaia «Oaoie/aneee oieaa?neoao» Na.no. 1-e Iaaeaeoia?iaeiie
iao/ii-i?aeoe/aneie eiioa?aioeee.- Iaeanna, 1996.-*.1.-N.33-35.

7. O a a a i ? i a I. A. Aneiioioe/aneia iiaaaeaiea ?aoaiee iaeiiai
eeanna iaeeiaeiuo aeeooa?aioeeaeueiuo o?aaiaiee n-ai ii?yaeea//
Aeeoa?aioe?aeueii-ooieoe?iiaeuei? ??aiyiiy oa ?o canoinoaaiiy:
Anaoe?a?inueea eiioa?aioe?y, 1996. i.*a?i?aoe?.-Ee?a, 1996. — N.198.

8. O a a a i ? i a I. A., ? a o o o i a A. I. Aneiioioe/aneia
iiaaaeaiea ?aoaiee iaeiiai eeanna iaeeiaeiuo aeeooa?aioeeaeueiuo
o?aaiaiee n-ai ii?yaeea //V I?aeia?iaeia iaoeiaa eiioa?aioe?y ?i.
aeaaeai?ea I.E?aa/oea. — E., 1996. — N.135.

9. O a a a i ? i a I. A. I?aaeeuei? iiiioiii? ?ica’ycee iaeiiai eeano
iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue n-ai ii?yaeeo//Ia?niaeoeai?
iai?yie ?icaeoeo AIE I?e/i?iiii?nueeiai ?aa?iio: Oace aeiiia?aeae
iaeanii? iaoeiai-i?aeoe/ii? eiioa?aioe??. — Ieeiea?a, 1996. -N. 101-102.

10. O a a a i ? i a I. A., ? a o o o i a A. I. Ia aneiioioeea
?aoaiee iaeeiaeiuo aeeooa?aioeeaeueiuo o?aaiaiee n-ai ii?yaeea//
Aneiioioe/i? oa ye?ni? iaoiaee a oai??? iae?i?eieo eieeaaiue:
I?aeia?iaeia eiioa?aioe?y, O?ao? Aiaietha?anuee? /eoaiiy.-
E.-1997.-N.55.

AIIOAOe?ss

— ai ii?yaeeo a?eueo caaaeueiiai aeaeo.

— ai ii?yaeeo c iae?i?eiinoyie oeio Aiaeaia-Oaoea?a, aneiioioe/i?
cia?aaeaiiy iaeieeaieo ?ica’yce?a.

AIIIOAOeEss

I?iaeaia eco/aiey aneiioioe/aneiai iiaaaeaiey ?aoaiee iaeeiaeiuo
iaaaoiiiiiuo iaueiiaaiiuo aeeooa?aioeeaeueiuo o?aaiaiee o?aaeeoeeiiii
caieiaao iaeii ec oeaio?aeueiuo e i?eioeeieaeueii aaaeiuo iano a
ea/anoaaiiie oai?ee aeeooa?aioeeaeueiuo o?aaiaiee.

-?aoaiee enoiaeiiai o?aaiaiey, iieo/eoue aeey ieo ana aiciiaeiua
aneiioioe/aneea i?aaenoaaeaiey e iaiaoiaeeiua oneiaey nouanoaiaaiey
?aoaiee n oaeeie i?aaenoaaeaieyie. Aii?in i oaeoe/aneii eo nouanoaiaaiee
?aoaeny iooai naaaeaiey e aii?ino i nouanoaiaaiee en/acathueo ia
aaneiia/iinoe ?aoaiee o iaeioi?ie nenoaiu eaaceeeiaeiuo
aeeooa?aioeeaeueiuo o?aaiaiee, iieo/aiiie a ?acoeueoaoa i?aia?aciaaiey,
ii?aaeaeyaiiai iaeaeaiiuie aneiioioe/aneeie i?aaenoaaea-ieyie. A yoio
aii?in a naith i/a?aaeue ?aoaeny ia iniiaaiee ?acoeueoaoia ?aaio
A.A.Einoeia e A.I.Aaoooiaa.

-?aoaiee ?anniao?eaaaiuo a aeenna?oaoeee o?aaiaiee. Aieaa oiai,
onoaiiaeaiu iaiaoiaeeiua e aeinoaoi/iua oneiaey nouanoaiaaiey o ieo
?aoaiee n iieo/aiiuie aneiioioe/aneeie i?aaenoaaeaieyie.

— ai ii?yaeea n iaeeiaeiinoyie oeia Yiaeaia-Oaoea?a, aneiioioe/aneea
i?aaenoaaeaiey iaeieaaethueony ?aoaiee.

ANNOTATION

-solutions with obtained asymptotic representations are stated. The
research methodic worked out for the given class may be spread onto the
n-th order equations of the more ordinary type.

Key words: differential equations of the n-th order with nonlinearties
of the Emden-Fowler type, asymptotic representations of the
non-oscillation solutions.

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