Interval oscillation criteria for second order damped half-linear differential equations with forcing term

Abstract

By using an inequality due to Hardy, Littlewood and Polya and averaging functions, several interval oscillation criteria are established for the second-order damped half-linear differential equation with forcing term of the form (r(t)|y′(t)|α−1y′(t))′ + p(t)|y′(t)|α−1y′(t) + q(t)|y(t)|α−1y(t) = e(t) that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0,∞) , rather than on the whole half-line, where α > 0 . In particlar, several examples that dwell upon the importance of our results are also included. Mathematics subject classification (2000): 34C10, 34C15.