含导数项两端固定支撑的弹性梁方程的可解性  

Solvability of Elastic Beam Equation with Derivative Term and Fixed Supports at Both Ends

作　　者：瞿婧 李永祥 QU Jing;LI Yongxiang(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,兰州730070

出　　处：《吉林大学学报（理学版）》2023年第5期1014-1018,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061062,11661071).

摘　　要：用Leray-Schauder不动点定理,讨论四阶边值问题{u^((4))(x)=f(x,u(x),u′(x)),x∈[0,1],u(0)=u(1)=u′(0)=u′(1)=0的可解性,其中f:[0,1]×ℝ^(2)→ℝ连续.在允许非线性项f(x,u,v)关于u,v超线性增长的条件下,获得了该问题解的存在性和唯一性结果.By using the Leray-Schauder fixed point theorem,we discuss the solvability of the fourth-order boundary value problem {u^((4))(x)=f(x,u(x),u′(x)),x∈[0,1],u(0)=u(1)=u′(0)=u′(1)=0,where f:[0,1]×ℝ^(2)→ℝis continuous.The existence and uniqueness of solutions to the problem are obtained under the condition that the nonlinear term f(x,u,v)is allowed to grow superlinearly with respect to u,v.

关 键 词：弹性梁方程 存在唯一性 超线性增长 LERAY-SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]