Existence of Solutions of Periodic Boundary Value Problems for Impulsive Functional Duffing Equations at Nonresonance Case

oleh: Yuji Liu, Xingyuan Liu

Format: Article
Diterbitkan: SpringerOpen 2008-11-01

Deskripsi

This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: x′′(t)+αx′(t)+βx(t)=f(t,x(t),x(α1(t)),…,x(αn(t))), a.e.  t∈[0,T], Δx(tk)=Ik(x(tk),x′(tk)), k=1, …,m, Δx′(tk)=Jk(x(tk),x′(tk)), k=1,…,m, x(i)(0)=x(i)(T), i=0,1. Sufficient conditions are established for the existence of at least one solution of above-mentioned boundary value problem. Our method is based upon Schaeffer's fixed-point theorem. Examples are presented to illustrate the efficiency of the obtained results.