Oscillation of even order nonlinear functional differential equations with damping

Abstract

Abstract This paper is concerned with a class of even order nonlinear damped differential equations \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\begin{gathered} {\text{ }}x^{(n)} (t) + p(t)x^{(n - 1)} (t) \hfill \\ + f\left( {t,x[\tau _{01} (t)],...,x[\tau _{0m} (t)],...,x^{(n - 1)} [\tau _{n - 11} (t)],...,x^{{\text{(n - 1)}}} [\tau _{n - 1n} (t)]} \right) = 0 \hfill \\ \end{gathered}$$ \end{document} where n is even and t≥t 0. By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results.