一类奇异边值问题解的存在性  

Solvability of Singular Second Order m-Point Boundary Value Problems

作　　者：何韬[1] 

机构地区：[1]西安交通大学理学院,陕西西安710049

出　　处：《江西师范大学学报（自然科学版）》2008年第3期317-321,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：甘肃省自然科学基金(3ZS051-A25-047)资助项目

摘　　要：为了讨论一类奇异边值问题解的存在性问题,首先得出与所研究奇异边值问题等价的积分算子方程,其次证明积分算子是全连续算子,最后运用Leray-Schauder原理,在f:[0,1]×R2→R满足Carathéodory条件且(1-t)e(t)∈L1(0,1)时,解决了这类奇异二阶m-点边值问题解的存在性问题,并获得了该类问题至少存在一个解的充分条件.In order to discuss the existence of solutions to singular boundary value problems of a class , the author proceeds the research to solve this type of problem by firstly constructing the integral equation of being equivalent to the problem , secondly proofing the integral equation being completely continuous, finally by using Lerary-Schauder＇ s principle , the existence of solutions for a singular second order m- point boundary value problems under f： [0, 1 ] ×R^2→R be a function satisfying Carathéodory＇ s conditions and, （ 1 - t ）e （ t ） ∈ L^1 （0, 1 ）, a （ t ） ∈ L^1 [0, 1 ] be given, and a sufficient condition for the existence of solutions is given to singular boundary value problems of a class .

关 键 词：奇异边值问题 LERAY-SCHAUDER原理 Carathéodory条件 格林函数 

分 类 号：O175.8[理学—数学]