Interval oscillation of a general class of second-order nonlinear differential equations with nonlinear damping

Abstract

The paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms. Several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions. Examples are also given to illustrate the results. In particular, it is shown that under some very mild conditions on k 1 , k 2 , and f the equation ( k 1 ( x , x ′ ) ) ′ + cos tk 2 ( x , x ′ ) x ′ + sin tf ( x ) = 0 is oscillatory, which extends the result obtained by Kwong and Wong (J. Math. Anal. Appl. 288 (2003) 15).