Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations

Abstract

New oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the form (r(t)Φα(x′))′+q(t)Φα(x)+∑k=1nqk(t)Φβk(x)=e(t),t≠θix(θi+)=aix(θi),x′(θi+)=bix′(θi) where Φγ(s):=|s|γ−1s and β1>β2>⋯>βm>α>βm+1>⋯>βn>0. If α=1 and the impulses are dropped, then the results obtained by Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549–560] are recovered. Examples are given to illustrate the results.