Positive solutions of BVPs for third-order discrete nonlinear difference systems

被引：4

作者：

Zhang R. ^{[1
]}

机构：

[1] School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu

来源：

Journal of Applied Mathematics and Computing | 2011年 / 35卷 / 1-2期

关键词：

Cone; Discrete system; Fixed point; Multiplicity; Nonexistence; Positive solution;

D O I：

10.1007/s12190-010-0378-7

中图分类号：

学科分类号：

摘要：

This paper is concerned with the following system Δ 3u i(k)+fi (k,u1(k),u2(k),⋯, un(k))=0, k ψ [0,T], i=1,2, ⋯ ,n, with the Dirichlet boundary condition ui(0)=ui (1)=uii(T+3)=0, quad{}i=1,2,⋯,n. Some results are obtained for the existence, multiplicity and nonexistence of positive solutions to the above system by using nonlinear alternative of Leray-Schauder type, Krasnosel'skii's fixed point theorem in a cone and Leggett-Williams fixed point theorem. In particular, it proves that the above system has N positive solutions under suitable conditions, where N is an arbitrary integer. © 2010 Korean Society for Computational and Applied Mathematics.

引用

页码：551 / 575

页数：24

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