高阶微分方程奇异半正的m-点边值问题(英文)

Singular semi-positone m-point boundary value problems of higher order differential equations

我们利用不动点指数理论研究高阶微分方程奇异半正的m 点边值问题多重正解的存在性。所讨论问题中的非线性项目f(t,x)可以在x=0,t=0和t=1中奇异。其主要结果为以下三个定理:定理2.1 给出了奇异边值问题(1)至少有一个正解存在的充分条件。定理2.2 给出了奇异边值问题(1)至少有二个正解存在的充分条件。定理2.3 给出了奇异边值问题(1)至少有三个正解存在的充分条件。

<Abstrcat>In this paper,we use the fixed point index theory to investigate the existence of multiple positive solutions for some singular semi-positone m-point boundary value problems of higher order differential equations. In addition,we will assume that the nonlinearity f(t,x) may be singular at x=0,t=0 and /or t=1. The main results of this paper are the following three theorems:Theorem 2.1 Gives sufficient conditions which the boundary value problem (1) has at least one positive solutions.Theorem 2.1 Gives sufficient conditions which the boundary value problem (1) has at least two positive solutions.Theorem 2.3 Gives sufficient conditions which the boundary value problem (1) has at least three positive solutions.