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Zbl 1103.34017
Jaroš, Jaroslav; Takaŝi, Kusano; Tanigawa, Tomoyuki
Nonoscillatory half-linear differential equations and generalized Karamata functions.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 64, No. 4, A, 762-787 (2006). ISSN 0362-546X

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 $$\bigl(p(t)|y'|^{\alpha-1}y'\bigr)'+q (t)|y|^{\alpha-1}y=0.$$
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: half-linear differential equation; nonoscillation; slowly varying function; regular variation

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