Multiple positive solutions for semi-positone m-point boundary value problems

被引：0
|
作者：
Zhai, Cheng-bo [1 ]
Yang, Cheng [2 ]
机构：
[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China
[2] Shanxi Univ, Coll Business, Taiyuan 030031, Shanxi, Peoples R China
来源：
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2011年 / 27卷 / 03期
关键词：
Multiple positive solutions; cone; semi-positone m-point boundary value problem; concave functional; parameter; EXISTENCE;
D O I：
10.1007/s10255-009-6180-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u" (t) + lambda f(t, u) = 0, t is an element of (0, 1), u'(0) = (m-2)Sigma(i=1) b(i)u'(xi(i)), u(1) = (m-2)Sigma(i=1) a(i)u(xi(i)), where lambda > 0 is a parameter, 0 < xi(1) < xi(2) < ... <xi(m-2) < 1 with 0 < (m-2)Sigma(i-1) a(i) < 1, (m-2)Sigma(i-1) b(i) < 1, a(i), b(i) is an element of [0,infinity) and f( t, u) >= - M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.
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页码：419 / 426
页数：8
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