高阶微分方程多点边值问题的正解存在性

Positive Solutions to Multipoint Higher Order Boundary Value Problem

非线性二阶微分方程多点边值问题的研究由Il'in及Moiseev始创.自此以后,通过应用Leray-Schauder定理,Leray-Schauder非线性选择定理,或重合度理论,许多学者研究更为普遍的非线性多点边值问题,比如,Gupta,Feng andWebb,Marano.本文主要利用Krasnosel'skii不动点定理,研究了在超线性和次线性的情况下,高阶微分方程多点边值问题的正解存在性,并得到了两个正解存在性定理及一个正解不存在性定理.

The study of multipoint boundary value problem for nonlinear second-order ordinary differential equations was initiated by Ilin and Moiseev.Since then,by applying the Leray-Schauder continuation theorem,nonlinear alternative of Leray-Schauder,or coincidence degree theory,many authors studied more general nonlinear multipoint boundary value problem, for example,Gupta,Feng and Webb,Marano.In this paper,by using Krasnoselskii fixed point theorem,we study positive solutions to multipoint higher order boundary value problems and get two existence theorems and one nonexistence theorem.