Asymptotic behavior of solutions of second-order nonlinear delay differential equations with impulses

摘要

This paper is concerned with second-order nonlinear delay differential equations with impulses of the form (r(t)x′(t))′+p(t)x′(t)+f(t,x(t−δ))=0,t≠tk,x′(tk+)=Ik(x′(tk)),x(tk+)=Jk(x(tk)),t=tk,k=1,2,…,t≥t0. By impulsive differential inequality and Riccati transformation, sufficient conditions of asymptotic behavior of all solutions of second-order nonlinear delay differential equations with impulses are obtained. Some examples are also inserted to illustrate the impulsive effect.