Oscillation Criteria for Forced Second Order Mixed Type Quasilinear Delay Differential Equations

Abstract

This article presents new oscillation criteria for the second-order delay differential equation $$(p(t) (x'(t))^{alpha})' + q(t) x^{alpha}(t - au) + sum_{i = 1}^{n} q_{i}(t) x^{alpha_{i}}(t - au) = e(t)$$ where $au geq 0$, $p(t) in C^1[0, infty)$, $q(t),q_{i}(t), e(t) in C[0, infty)$, $p(t) > 0$, $alpha_1 >dots > alpha_{m} > alpha > alpha_{m+1} > dots > alpha_{n} > 0 (n > mgeq 1)$, $alpha_1, dots , alpha_{n}$ and $alpha$ are ratio of odd positive integers. Without assuming that $q(t), q_{i}(t)$ and $e(t)$ are nonnegative, the results in [6,8] have been extended and a mistake in the proof of the results in [3] is corrected