Oscillation of higher-order half-linear neutral differential equations

Abstract

Abstract In this paper, we establish some new oscillation criteria for the higher-order half-linear neutral differential equation [ a ( t ) ( [ x ( t ) + p ( t ) x ( σ ( t ) ) ] ( n − 1 ) ) γ ] ′ + q ( t ) x γ ( τ ( t ) ) = 0 . $$\left[ {a(t)\,\,\left( {[x(t) + p(t)x(\sigma (t))]^{(n - 1)} } \right)^\gamma } \right]^\prime + q(t)x^\gamma (\tau (t)) = 0.$$ An example is given to illustrate the main results.