Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 105, pp. 1-8.
Title: A Riccati technique for proving oscillation of a half-linear equation
Author: Pavel Rehak (Academy of Sciences, Brno, Czech Republic)
Abstract:
In this paper we study the oscillation of solutions to
the half-linear differential equation
$$
(r(t)|y'|^{p-1}\hbox{sgn} y)'+c(t)|y|^{p-1}\hbox{sgn} y=0,
$$
under the assumptions $\int^\infty r^{1/(1-p)}(s)\,ds<\infty$,
$r(t)>0$, $p>1$.
Our main tool is a Riccati type transformation for using the
so called "function sequence technique".
This method leads to new and to known oscillation and comparison
results. We also give an example that illustrates our results.
Submitted May 12, 2008. Published August 06, 2008.
Math Subject Classifications: 34C10.
Key Words: Half-linear differential equation; Riccati technique;
oscillation criteria.