周友明.Banach空间中非线性奇异两点边值问题的多重正解[J].数学研究及应用,2006,26(1):1~8 |
Banach空间中非线性奇异两点边值问题的多重正解 |
Multiple Positive Solutions of Nonlinear Singular Two-point Boundary Value Problems in Banach Spaces |
投稿时间:2003-10-16 |
DOI:10.3770/j.issn:1000-341X.2006.01.001 |
中文关键词: 奇异边值问题 Banach空间 正解 不动点定理. |
英文关键词:singular boundary value problem Banach space positive solution fixed point theorem. |
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中文摘要: |
本文研究Banach空间E中非线性奇异边值问题-x''=f(t,x), t∈(0,1), a1x(0)-a2x'(0)=θ, b1x(0)-b2x'(1)=θ.其中θ是E中的零元素, f({t,x})在端点t=0和t=1处具有奇性. 利用不动点定理获得了该问题至少有两个正解的结果. |
英文摘要: |
In this paper , we study the nonlinear singular boundary value problems in Banach spaces: -x''=f(t,x), t∈(0,1), a1x(0)-a2x'(0)=θ, b1x(0)-b2x'(1)=θ, where θ denotes the zero element of E, E is a real Banach space, and f({t,x}) is allowed to be singular at both end point t=0 and t=1. We show the existence of at least two positive solutions of this problem. |
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