二阶常微分方程无穷多点边值问题的正解

Abstract

Abstract:

Let α _i∈[0, ∞), ξ _i ∈ (0,1) and ∑^∞_i=1α _i ξ_i<1. We study the existence of positive solutions to the boundary value problem

u''+a(t) f(u)=0, t ∈(0, 1),
u(0)=0, u(1)= ∑^∞_{i =1} α _iu ( ξ _i) ,
where α ∈ C([0, 1], [0, ∞)), and f:[0, ∞) → [0, ∞) is continuous. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed-point theorem in cones.

Key words: ∞-point boundary value problem, Positive solution, Cone, Fixed point

CLC Number:

34B15

Cite this article

MA Ru-Yun, FAN Hong-Xia, HAN Xiao-Ling. Positive Solutions of Nonlinear ∞-point Boundary Value Problems[J].Acta mathematica scientia,Series A, 2009, 29(3): 699-706.

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Positive Solutions of Nonlinear ∞-point Boundary Value Problems

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