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.
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)
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)。
关键词
四阶微分方程
正解
边值问题
不动点定理
fourth-order differential equation
positive solution
boundary value problem
fixed point theorem
