一阶非线性脉冲微分方程边值问题解的存在性

Existence of Solutions for First-order Nonlinear Impulsive Differential Equations with Boundary Value Problems

利用Schaefer不动点定理,研究了一阶非线性脉冲微分方程边值问题{u'(t)=f(t,u(t)),t∈[0,T]\{tk},k=1,…,m,u(tk+)=u(tk-)+Ik(u(tk)),k=1,…,m,u(0)=βu(T)解的存在性,所得结果推广了已有的结论.

In this paper,the existence of solutions for the following nonlinear first order impulsive differential equations with boundary value problems is considered{u＇（t） = f（t,u（t））,t ∈[0,T]／{ tk},k = 1,…,m,u（tk＋） = u（tk-） ＋ Ik（u（tk））,k = 1,…,m,u（0） = βu（T）.New criteria are established based on Schaefer＇s fixed-point theorem.The results extend some known results.