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

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 $int^infty r^{1/(1-p)}(s),ds0$, $p>1$. 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.

Keywords

• Half-linear differential equation
• Riccati technique
• oscillation criteria