On the oscillation of certain second-order nonlinear differential equations

Abstract

In this paper, oscillation criteria for the nonlinear second-order ordinary differential equation

$$\text{r(t)Ψ}\text{x(t)}\text{x′(t)}{}^{\mathrm{p-2}}\text{x′(t)}\text{′+c(t)f}\text{x(t)}\text{=0}$$

are given. The results extend the integral averaging technique and include earlier results. Our methodology is somewhat different from that of previous authors.