Double solutions of boundary value problems for 2mth-order differential equations and difference equations

被引：17

作者：

Graef, JR ^{[1
]}

Henderson, J

机构：

[1] Univ Tennessee, Dept Math, Chattanooga, TN 37403 USA

[2] Baylor Univ, Dept Math, Waco, TX 76798 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2003年 / 45卷 / 6-9期

关键词：

boundary value problem; Green's function; multiple solutions; SYMMETRIC POSITIVE SOLUTIONS; ORDERED BANACH-SPACES; MULTIPLE SOLUTIONS; TWIN SOLUTIONS; FIXED-POINTS; EXISTENCE;

D O I：

10.1016/S0898-1221(03)00063-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A double fixed-point theorem is applied to obtain the existence of at least two positive solutions for the boundary value problem, (-1)(m)y((2m)) (t) = f (y(t)), t is an element of [0, 1], y((2i)) (0) = y((2i+1)) (1) = 0, 0 less than or equal to i less than or equal to m - 1. It is later applied to obtain the existence of at least two positive solutions for the analogous discrete boundary value problem, (-1)(m)Delta(2m)u(k) = g(u(k)), k is an element of {0,...,N}, Delta(2i)u(0) = Delta(2i+1)u(N + 1) = 0, 0 less than or equal to i less than or equal to m - 1. (C) 2003 Elsevier Science Ltd. All rights reserved.

引用

页码：873 / 885

页数：13

共 21 条

[1]

Agarwal R.P., 1999, POSITIVE SOLUTIONS D

[2]

Avery R.I., 2001, Comm. Appl. Nonlinear Anal, V8, P27

[3] Three positive fixed points of nonlinear ordered Banach spaces [J].