一类四阶边值问题解的存在唯一性  

Existence and Uniqueness of Solutions for a Class of Fourth Order Boundary Value Problems

作　　者：邓瑞娟[1] 崔洪瑞 DENG Ruijuan;CUI Hongrui(Department of Basic,Wuhu Institute of Technology,Wuhu 241003,Anhui,China;GDPU Undergraduate School of Medical Business,Guangdong Pharmaceutical University,Guangzhou,510006,Guangdong,China)

机构地区：[1]芜湖职业技术学院基础部,安徽芜湖241003 [2]广东药科大学医药商学院,广东广州510006

出　　处：《山西师范大学学报（自然科学版）》2022年第4期1-4,共4页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：安徽省高校自然科学研究重点项目(KJ2020A0916);安徽省高校质量工程项目(2020jxtd281).

摘　　要：首先,运用傅里叶分析法和Leray-Schauder不动点定理得出了一类具有完全非线性项的四阶微分方程边值问题解的存在性,其中Lu(t)为四阶线性常微分算子;其次,在非线性项f满足lipschitz条件下证明了方程有唯一解;最后,给出了结论应用的具体实例.Firstly,by using Fourier analysis method and Leray-Schauder fixed point theorem,the existence of solutions for boundary value problems of a class of Fourth-order Differential Equations with completely nonlinear terms is obtained,where Lu(t)is a fourth-order linear ordinary differential operator;Secondly,it is proved that the equation has a unique solution under the condition that the nonlinear term f satisfied Lipschitz;Finally,an example of the application of the conclusion is given.

关 键 词：完全四阶边值问题 傅里叶分析法 LERAY-SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]