Electron. J. Diff. Eqns., Vol. 2008(2008), No. 105, pp. 1-8.

A Riccati technique for proving oscillation of a half-linear equation

Pavel Rehak

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 6, 2008.
Math Subject Classifications: 34C10.
Key Words: Half-linear differential equation; Riccati technique; oscillation criteria.

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Pavel Rehak
Institute of Mathematics, Academy of Sciences
Zizkova 22, CZ61662 Brno, Czech Republic
email: rehak@math.muni.cz

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