Acta mathematica scientia, Series B >
TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS
Received date: 2007-07-14
Revised date: 2009-08-27
Online 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).
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.
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 . DOI: 10.1016/S0252-9602(11)60205-1
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