无穷区间上奇异边值问题正解的存在性
Existence of Positive Solutions for Singular Boundary Value Problems on the Infinite Interval
DOI: 10.12677/AAM.2017.69140, PDF,    科研立项经费支持
作者: 王 克, 王 颖：临沂大学数学与统计学院，山东 临沂
关键词: 正解；锥；不动点；无穷区间；Positive Solutions； Cone； Fixed Points； Infinite Interval
摘要: Banach空间中的微分方程理论是非线性泛函分析的重要分支，奇异方程边值问题是微分方程学科的组成部分，处于微分方程理论和线性及非线性泛函分析的交叉结合点上，广泛存在于弹簧的振动、梁的非弹性振动、种群生态系统等自然界的各种数学模型中，本文主要应用锥上的不动点理论，通过建立特殊的空间和范数，在非线性项f奇异的条件下，讨论了无穷区间上一类微分方程边值问题解的存在性，获得了方程至少存在一个正解的结论。本文的结果在一定程度上推广了奇异和非奇异条件下的许多已知结果。
Abstract: The theory of differential equations in Banach spaces is an important branch of nonlinear analysis. The boundary value problem of differential equation is the component of the differential equation subject, which is in the intersection of differential equation theory and linear and nonlinear functional analysis. It exists widely in various mathematical models of nature, such as spring vibration, inelastic vibration of beams and population ecosystem. In this paper, by using the fixed point theory in the cone with a special norm and space, the authors discuss the existence of positive solutions for a class of boundary value problems of differential equation on the infinite interval and obtain that the equation has at least one positive solution. The results improve many known results including singular and non-singular cases to a certain extent.
文章引用：王克, 王颖. 无穷区间上奇异边值问题正解的存在性[J]. 应用数学进展, 2017, 6(9): 1151-1162. https://doi.org/10.12677/AAM.2017.69140

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