抽象空间中n阶m点边值问题的正解
首发时间:2009-06-03
摘要:本文讨论了Banach空间中一类n阶m点边值问题的一个正解和两个正解的存在性,首先给出定理证明中所需要的范数形式的锥拉伸与压缩不动点定理,进而将这类n阶m点边值问题转化为积分方程,建立一个严格集压缩算子,然后利用锥拉伸与压缩不动点定理证明了这类n阶m点边值问题的一个正解和两个正解的存在性结果,并且最后给出一个例子来说明主要结果。
关键词: n阶m点边值问题 正解 Banach空间 不动点定理
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Positive Solutions For n th-order m-point Boundary Value Problem in a Banach Space
Abstract:In this paper, the existence of one and two positive solutions for a class of nth order m-point boundary value problem are obtianed. First, fixed-point theorem of norm is given, then we change the nth order m-point boundary value problem into integral equation, and construct a strict constraction operator. The existence results of one and two positive solutions for this a class of nth order m-point boundary value problem are proved. Finally, an example is given to demostrate the main result of this paper.
Keywords: nth-order m-point boundary value problem Positive solutions Banach space Fixed point theorem.
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