带有脉冲的二阶多点微分方程的边值问题

Boundary Value Problems for Second Order Multi-Point Difference Equations with Impulses

研究了一类带有脉冲的二阶多点微分方程的边值问题,将以往所研究的方程的脉冲项和边界条件做了推广,对其限制条件进行了修改,并且在脉冲项都含有一阶导数的情形下运用Leray-Schauder不动点定理探讨了该类问题解的存在性.对非线性项和脉冲项做了一些假设,证明了方程的解集有一个不依赖于参数λ的先验界,进而得到结论:方程至少有一个解.最后通过一个实例说明了结论的应用.

The existence of solutions for multi-point boundary value problem of second-order impulsive differential equations was investigated. The boundary value conditions and impulsive term were extended. In the case of the impulsive term with the first derivative, the new conclusions about the existence of the solution are obtained via Leray-Schauder fixed-point theorem. It is proved that when the nonlinear term and impulsive term with some assumptions, a priori bounds for the solutions set of the differential equation doesn＇t depend on the parameters 2. It draws the conclusion that the differential equation has one solution at least. At last, the material example shows the application of the results.