一类二阶微分方程Riemann-Stieltjes积分边值问题的非平凡解  

Nontrivial Solutions to Riemann-Stieltjes Integral Boundary Value Problems for a Class of Second-order Differential Equations

作　　者：张巧 柏仕坤 ZHANG Qiao;BAI Shikun(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《湖州师范学院学报》2025年第2期8-18,共11页Journal of Huzhou University

基　　金：重庆市自然科学基金项目(cstc2020jcyj-msxmX0123)。

摘　　要：运用拓扑度理论研究二阶微分方程Riemann-Stieltjes积分边值问题非平凡解的存在性。将该问题转化为与之等价的积分方程,在合适的空间构造算子方程,并借助不动点定理获得该算子不动点的存在性,进而获得原问题的非平凡解。This paper employs topological degree theory to investigate the existence of nontrivial solutions for a class of second-order differential equations associated with Riemann-Stieltjes integral boundary value problems.Firstly,the problem is reformulated as an equivalent integral equation.Next,by applying the fixed point theorem,the existence of fixed points for this operator is established,which subsequently yields the existence of nontrivial solutions to the original problem.

关 键 词：边值问题 非平凡解 拓扑度 

分 类 号：O175.1[理学—数学]