一类四阶常微分方程三点边值问题正解的存在性与稳定性分析研究  

Analysis of the existence and stability of positive solutions for a class of fourth-order ordinary differential equations with three-point boundary conditions

作　　者：杜政澔 朱会娟 茹原芳 DU Zhenghao;ZHU Huijuan;RU Yuanfang(School of Mathematics,Hohai University,Nanjing 211100,China;College of Science,China Pharmaceutical University,Nanjing 211198,China)

机构地区：[1]河海大学数学学院,江苏南京211100 [2]中国药科大学理学院,江苏南京211198

出　　处：《海南大学学报(自然科学版中英文)》2025年第1期81-90,共10页Natural Science of Hainan University

基　　金：国家自然科学基金项目(12001162);中央高校基本科研业务费项目(B240205026);江苏省研究生科研与实践创新计划项目(KYCX24_0821)。

摘　　要：研究了一类四阶常微分方程三点边值问题正解的存在性与稳定性。首先,给出了相应格林函数的性质和估计。其次,结合这些估计,利用Krasnosel'skii与Leggett-Williams不动点定理,讨论带有势函数的四阶三点边值问题正解的存在性,并考虑了扰动项在不同取值范围内对1个解、2个解和3个解存在性的影响。此外,还系统地分析了方程解在特定扰动下的Ulam-Hyers稳定性。最后,通过实例数值模拟,进一步验证了所提出结果的合理性和实际应用价值,充分展示了理论分析在实际问题中的重要性和有效性。In the report,the existence and stability of the positive solutions for a class of fourth-order ordinary differential equations with three-point boundary value problems were analyzed.Firstly,the properties and estimates of the corresponding Green's function were proposed;secondly,based on these estimates,Krasnosel'skii and Leggett-Williams fixed point theorems were used to discuss the existence of the positive solutions for the fourth-order three-point boundary value problem with a weight function,and the effects of the perturbation term within the different value ranges on the existence of one,two,and three solutions were also considered;thirdly,the Ulam-Hyers stability of the solutions under specific perturbations was systematically analyzed;finally, the numerical simulations were performed to verify the reasonableness and practical valueof the proposed results, and which demonstrated the importance and effectiveness of the theoretical analysis inpractical applications.

关 键 词：四阶微分方程 正解 边值问题 不动点定理 

分 类 号：O175.8[理学—数学]