Oscillation of second-order nonlinear noncanonical dynamic equations with deviating arguments

Abstract

The purpose of this paper is to establish some new criteria for the oscillation of the second-order nonlinear noncanonical dynamic equation  $(a(t)x^{\Delta}(t))^{\Delta} + q(t)x^{\beta}(g(t)) = 0$ under the condition $\int^{\infty}_t \frac{1}{a(s)} \Delta s<\infty$. The authors consider both delay and advanced equations. Anexample of Euler type equations is provided to illustrate the significance of the main results.