Article
MSC:
34B10,
34B15,
34K10,
34K45,
47N20 | MR 2563123 | Zbl 1212.34184 | DOI: 10.1007/s10492-009-0032-6
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Keywords:
periodic boundary value problem; impulsive differential equation; fixed-point theorem; growth condition
periodic boundary value problem; impulsive differential equation; fixed-point theorem; growth condition
Summary:
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation $$ \begin{cases} x'(t)=f(t,x(t),x(\alpha _1(t)),\cdots ,x(\alpha _n(t))) \text {for a.e.} \ t\in [0,T], \Delta x(t_k)=I_k(x(t_k)), \ k=1,\cdots ,m, x(0)=x(T). \end{cases} $$ We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin's continuation theorem. Examples are presented to illustrate the main results.
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