Property (A) of third-order advanced differential equations

Abstract

Abstract In the paper we offer criteria for property (A) of the third-order nonlinear functional differential equation with advanced argument $(a(t)(x'(t))^\gamma )'' + p(t)f(x(\sigma (t))) = 0,$, where $\mathop \smallint \limits^\infty a^{ - 1/\gamma } (s)ds = \infty $. We establish new comparison theorems for deducing property (A) of advanced differential equations from that of ordinary differential equations without deviating argument. The presented comparison principle fill the gap in the oscillation theory.