二阶非线性积-微分方程边值问题解的存在性  

The Exsitence of Solutions for the Boundary Value Problem of Nonlinear Second Order Integro-differential Equations

作　　者：尚亚亚 李永祥[1] SHANG Yaya LI Yongxiang(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gans)

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：《四川师范大学学报（自然科学版）》2016年第6期833-837,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11261053);甘肃省自然科学基金(1208R-JZA129)

摘　　要：讨论二阶积-微分方程边值问题{-u″(t)=f(t,u(t),(Su)(t)),t∈[0,1],u(0)=0,u(1)=0解的存在性,其中S为Fredholm型积分算子.在非线性项f(t,u,v)满足较弱的单调性条件下,建立了上下解定理,然后用该上下解定理,得到了一些存在性结果.特别在不要求f非负的一般情形下,用上下解方法获得了正解的存在性结果.In this paper,we study the exsistence of solutions for the boundary value problem of second order integro-differential equations {-un（t）=f（t,u（t））,（Su（t））,t∈[0,1],∪u（0）=0,u（1）=0}where S is the Fredholm integral operator,with a weaker monotonicity condition for f（t,u,v）,we establish an upper and lower solution theorem by which some exsistence results are obtained.Moreover,under the condition without requiring the nonlinear term f is non-negative,we obtain the existence of positive solutions for the problem via the upper and lower method.

关 键 词：二阶积-微分方程 极大值原理 上解 下解 正解 

分 类 号：O175.8[理学—数学]