Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations

Abstract

We are concerned with the oscillatory and nonoscillatory behavior of solutions of even-order quasilinear functional differential equations of the type , where and are positive constants, and are positive continuous functions on , and is a continuously differentiable function such that , . We first give criteria for the existence of nonoscillatory solutions with specific asymptotic behavior, and then derive conditions (sufficient as well as necessary and sufficient) for all solutions to be oscillatory by comparing the above equation with the related differential equation without deviating argument.