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Multiple Positive Solutions for Semi-positone m-point Boundary Value Problems 被引量:1

Multiple Positive Solutions for Semi-positone m-point Boundary Value Problems
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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) + λf (t, u) = 0, t ∈ (0, 1), u (0) = sum (biu (ξ i )) from i=1 to m-2, u(1)= sum (aiu(ξ i )) from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞) 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. 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) + λf (t, u) = 0, t ∈ (0, 1), u (0) = sum (biu (ξ i )) from i=1 to m-2, u(1)= sum (aiu(ξ i )) from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞) 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.
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第3期419-426,共8页 应用数学学报(英文版)
基金 Supported by Fund of National Natural Science of China (No. 10371068) Science Foundation of Business College of Shanxi University (No. 2008053)
关键词 Multiple positive solutions CONE semi-positone m-point boundary value problem concave functional PARAMETER Multiple positive solutions, cone, semi-positone m-point boundary value problem,concave functional, parameter
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