二阶脉冲微分方程m-点边值问题正解的存在性

The Existence of Positive Solutions for m-point Boundary Value Problem of Second Order Impulsive Differential Equations

讨论了一类非线性项与x'(t)有关的二阶脉冲微分方程的m-点边值问题,在对非线性项不作连续性要求,且f是一个Quasi-Carathéodory函数的条件下,利用锥拉伸与锥压缩不动点定理获得该问题正解的存在性定理.作为应用,给出了实例.

In this paper,a class of m-point boundary value problem of second-order impulsive differential equation with the first derivative is discussed.Here,the continuity of the nonlinear term f is not demanded,but a Quasi-Carathéodory condition is needed.The existence of the solution of the problem is obtained by using the fixed point theorem of cone expansion and compression.As an application,an example is given at the end of the paper.