TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

doi:10.1016/S0252-9602(11)60205-1

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 29-38.doi: 10.1016/S0252-9602(11)60205-1

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

李宇华|梁占平

School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

收稿日期:2007-07-14 修回日期:2009-08-27 出版日期:2011-01-20 发布日期:2011-01-20
基金资助:
Project supported by the National Natural Science Foundation of China (11071149, 10771128) and the NSF of Shanxi Province (2006011002, 2010011001-1).

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

LI Yu-Hua, LIANG Zhan-Ping

School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Received:2007-07-14 Revised:2009-08-27 Online:2011-01-20 Published:2011-01-20
Supported by:
Project supported by the National Natural Science Foundation of China (11071149, 10771128) and the NSF of Shanxi Province (2006011002, 2010011001-1).

摘要/Abstract

摘要：

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: −u′′(t) = λf(t, u(t)) for all t ∈(0, 1) subjecting to u(0)=0 and αu(η)=u(1), where η∈(0,1), α∈[0,1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t=0, t=1, and u=0. By the fixed point index theory and approximation method, we establish that there exists λ^∗∈ (0,+1], such that the above problem has at least two positive solutions for any λ ∈ (0, λ^∗) under certain conditions on the nonlinear term f.

关键词: Three-point singular boundary value problem, positive solutions, fixed point index

Abstract:

Key words: Three-point singular boundary value problem, positive solutions, fixed point index

中图分类号:

47H10

李宇华, 梁占平. TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS[J]. 数学物理学报(英文版), 2011, 31(1): 29-38.

LI Yu-Hua, LIANG Zhan-Ping. TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS[J]. Acta mathematica scientia,Series B, 2011, 31(1): 29-38.

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TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

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