一类完全二阶积-微分方程边值问题解的存在性  

Existence of Solutions for Boundary Value Problem of Fully Second-Order Integro-Differential Equations

作　　者：王婷婷 李永祥 WANG Tingting;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu)

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）》2024年第4期562-568,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(12061062和11661071)。

摘　　要：讨论完全二阶积-微分方程边值问题{-u″(t)=f(t,u(t),u′(t),Tu(t),Su(t)),t∈[0,1],u(0)=u(1)=0解的存在性,其中f:[0,1]×R^(4)→R连续,T、S分别为Volterra型与Fredholm型积分算子.在非线性项f(t,x,y,z,p)满足一些适当的不等式条件下,应用上下解方法与截断函数技巧获得该问题解的存在性.特别地,在不假定非线性项f(t,x,y,z,p)非负的一般情形下得到该问题正解的存在性.This paper discusses some existence results of solutions for such a problem{-u″(t)=f(t,u(t),u′(t),Tu(t),Su(t)),t∈[0,1],u(0)=u(1)=0,where f:[0,1]×R^(4)→R is continuous,while T,S are Volterra and Fredholm type integral operators.Under some proper inequality conditions of the nonlinear term f(t,x,y,z,p),the existence of solutions is obtained by using the method of upper and lower solutions and the truncating function technique.In particular,an existence result of positive solutions for such a problem is obtained without the nonnegativeness of f(t,x,y,z,p).

关 键 词：积-微分方程 边值问题 存在性 NAGUMO条件 上解 下解 

分 类 号：O175.6[理学—数学]