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二阶三点边值问题的正解 被引量:4

On Positive Solutions of Second-order Three-point Boundary Value Problem
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摘要 该文讨论了二阶三点边值问题-u″(t)=b(t)f(u(t))满足u′(0)=0,u(1)=αu(η)正解的存在性与多重性,其中常数α,η∈(0,1),f∈C([0,∞),[0,∞)),b∈C([0,1],[0,∞))且存在t_0∈[0,1]使b(t_0)>0.利用该问题相应的Green函数,将其转化为Hammerstein型积分方程,借助于锥上的不动点指数理论,给出了该问题单个正解和多个正解存在的与其相应线性问题的第一特征值有关的最佳充分性条件. In this paper, the existence of positive solutions of the second-order three-point boundary value problem -u"(t) = b(t)f(u(t)) for all t E [0, 1] subject to u'(0) = 0, u(1) = αu(η) is studied, where α, η ∈ (0, 1) are given, f ∈ C([0, ∞), [0, ∞)), b ∈ C([0, 1], [0, ∞)) and there exists to E [0, 1] such that b(to) 〉 0. The problem is transformed into the Hammerstein's integral equation with its corresponding Green's funtion. By applying the fixed point index theory, authors obtain the optimal sufficient conditions for the existence of single and multiple positive solutions of the above mentioned problem concerning the first eigenvalue of the relevant linear problem.
出处 《数学物理学报(A辑)》 CSCD 北大核心 2008年第2期373-382,共10页 Acta Mathematica Scientia
基金 山西省自然科学基金(20051005)资助
关键词 正解 不动点指数 第一特征值 Positive solutions Cone Fixed point index First eigenvalue.
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参考文献11

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