数学
数学分析
微分方程
常微分方程
斯特姆-刘维尔理论
边值问题
精确微分方程
一阶偏微分方程
作者
Zihan Li,Xu Shu,Tengyuan Miao
标识
DOI:10.1186/s13661-021-01574-x
摘要
Abstract In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with random impulses. Then, we get the equivalent integral equation of the random impulsive differential equation. Based on this integral equation, we use Dhage’s fixed point theorem to prove the existence of solutions to the equation, and the theorem is extended to the general second order nonlinear random impulsive differential equations. Then we use the upper and lower solution method to give a monotonic iterative sequence of the generalized random impulsive Sturm–Liouville differential equations and prove that it is convergent. Finally, we give two concrete examples to verify the correctness of the results.
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