Nonoscillatory half-linear differential equations and generalized Karamata functions

We introduce a natural generalization of the concept of regularly varying functions in the sense of Karamata, and show that the class of generalized Karamata functions is a well-suited framework for the study of the asymptotic behavior of nonoscillatory solutions of the half-linear differential equa...

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Bibliographic Details
Published in:Nonlinear analysis 2006-02, Vol.64 (4), p.762-787
Main Authors: Jaroš, Jaroslav, Takaŝi, Kusano, Tanigawa, Tomoyuki
Format: Article
Language:English
Subjects:
Exact sciences and technology
Half-linear differential equation
Mathematical analysis
Mathematics
Nonoscillation
Ordinary differential equations
Regular variation
Sciences and techniques of general use
Slowly varying function
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Summary:We introduce a natural generalization of the concept of regularly varying functions in the sense of Karamata, and show that the class of generalized Karamata functions is a well-suited framework for the study of the asymptotic behavior of nonoscillatory solutions of the half-linear differential equation of the type (A) ( p ( t ) | y ′ | α - 1 y ′ ) ′ + q ( t ) | y | α - 1 y = 0 .
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.05.045