Modified Riccati technique for half-linear differential equations with delay

We study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear differential equation. Our proofs are b...

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Bibliographic Details
Published in:Electronic Journal of Qualitative Theory of Differential Equations
Main Authors: Simona Fišnarová, Robert Marik
Format: Article
Language:English
Published: University of Szeged 2014-12-01
Subjects:
half-linear differential equation
delay equation
oscillation criteria
modified riccati technique
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=3344
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Summary:We study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear differential equation. Our proofs are based on a suitable estimate for the solution of the equation studied and on the modified Riccati technique, which, in ordinary case, appeared to be an effective replacement of the well known linear transformation formula.
ISSN:1417-3875

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