摘要
用Leray-Schauder不动点定理,讨论二阶非线性积-微分方程边值问题:{-u″(t)=f(t,u(t),Su(t)),t∈[0,1],u(0)=u(1)=0解的存在性与唯一性,其中f:[0,1]×ℝ^(2)→ℝ连续,S为Fredholm型积分算子.在非线性项f(t,x,y)满足适当的不等式条件下,获得了该问题解的存在性与唯一性,并把所得结果应用于弯曲弹性梁方程.
By using Leray-Schauder fixed-point theorem,we discuss the existence and uniqueness of solutions for the boundary value problems of nonlinear second-order integro-differential equation{-u″(t)=f(t,u(t),Su(t)),t∈[0,1],u(0)=u(1)=0,where f:[0,1]×ℝ^(2)→ℝis continuous,S is a Fredholm type integral operator.Under proper inequality conditions of the nonlinear term f(t,x,y),the existence and uniqueness of solutions of the problem are obtained,and the results are applied to bending elastic beam equation.
作者
王婷婷
李永祥
WANG Tingting;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)
出处
《吉林大学学报（理学版）》
CAS
北大核心
2022年第5期1036-1042,共7页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:12061062,11661071)。
关键词
积分-微分方程
边值问题
存在性与唯一性
不动点定理
弹性梁方程
integro-differential equation
boundary value problem
existence and uniqueness
fixed-point theorem
elastic beam equation
