一类四阶微分方程边值问题解的存在唯一性  

Existence and uniqueness of solutions of a class of fourth order differential equations BVPs

作　　者：赵娇 马如云 Zhao Jiao;Ma Ruyun(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《纯粹数学与应用数学》2021年第1期81-90,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11671322)。

摘　　要：为解决两端固定支撑弹性梁解的存在性及唯一性问题,运用Leray-Schauder延拓定理,研究一类非线性四阶常微分方程边值问题,当非线性项满足适当至多增长性条件时,得到解的存在性结果.进一步,当非线性项满足Lipschitz条件时,得到解的唯一性结果.In order to analyze the existence and uniqueness of solutions for clamped elastic beam at both ends.We study nonlinear fourth-order ordinary differential equations boundary value problems by using the Leray-Schauder continuation theorem.The existence of solutions are obtained when the nonlinear term satisfies the condition of proper utmost growth.In addition,the uniqueness of solutions are obtained when the nonlinear term satisfies the Lipschitz condition.

关 键 词：Carathéodory函数 WIRTINGER不等式 Leray-Schauder延拓定理 解的存在唯一性 

分 类 号：O175.8[理学—数学]