ASYMPTOTIC ANALYSIS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS IN THE FRAMEWORK OF REGULAR VARIATION

Under the assumptions thatp(t),q(t) are regularly varying functions satisfying condition ∫ a ∞ d t p ( t ) 1 α = ∞ , existence and asymptotic form of regularly varying intermediate solutions are studied for a fourth-order quasilinear differential equation ( p ( t ) | x ″ ( t ) | α − 1 x ″ ( t ) ) ″...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 19; no. 5; pp. 1415 - 1456
Main Authors Milošević, Jelena, Manojlović, Jelena V.
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2015
Subjects
Coefficients
Differential equations
Infinity
Mathematical functions
Sufficient conditions
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.19.2015.5048

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Summary:Under the assumptions thatp(t),q(t) are regularly varying functions satisfying condition ∫ a ∞ d t p ( t ) 1 α = ∞ , existence and asymptotic form of regularly varying intermediate solutions are studied for a fourth-order quasilinear differential equation ( p ( t ) | x ″ ( t ) | α − 1 x ″ ( t ) ) ″ ​ + q ( t ) | x ( t ) | β − 1 x ( t ) = 0 , α > β > 0. It is shown that the asymptotic behavior of all such solutions is governed by a unique explicit law. 2010Mathematics Subject Classification: Primary 34A34; Secondary 26A12. Key words and phrases: Regularly varying solutions, Slowly varying solutions, Asymptotic behavior of solutions, Positive solutions, Fourth order differential equations.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.19.2015.5048