Nonprincipal solutions in oscillation criteria for half-linear differential equations-Reference-Cited by-同舟云学术

Nonprincipal solutions in oscillation criteria for half-linear differential equations

Published:2010-03-01 Issue:1 Volume:47 Page:127-137
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
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Author:

Došlý Ondřej¹,Řezníčková Jana²

Affiliation:

1. 1 Masaryk University Department of Mathematics and Statistics Kotlářská 2 CZ-61137 Brno Czech Republic

2. 2 Tomas Bata University Department of Mathematics Nad Stráněmi 4511 760 05 Zlín Czech Republic

Abstract

We establish a new oscillation criterion for the half-linear second order differential equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x): = |x|^{p - 2} x,p > 1.$$ \end{document}

In this criterion, an integral term appears which involves a nonprincipal solution of a certain equation associated with (*).

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://www.akademiai.com/doi/pdf/10.1556/sscmath.2009.1120

Reference24 articles.

1. Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

2. Principal solutions and minimal sets of quasilinear differential equations;Cecchi M.;Dynam. Systems Appl.,2004

3. Cecchi, M., Došlá, Z. and Marini, M. , Half-linear Equations and Characteristic Properties of Principal Solutions, J. Differential Equations , 208 (2005), no. 2, 494–507. Mr 2006a :34095

4. Došlá, Z. and Došlý, O. , Principal Solution of Half-linear Differential Equation: Limit and Integral Characterization , Proceedings of the 8th Colloquium on the Qualitative Theory of Differential Equations (Szeged, 2008), no. 6, pp. 1–14.

5. Perturbations of the half-linear Euler-Weber differential equation;Došlý O.;J. Math. Anal. Appl.,2006

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