无穷区间上奇异边值问题正解的存在性.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(9), 1151-1162 Published Online December 2017 in Hans. /journal/aam /10.12677/aam.2017.69140 Existence of Positive Solutions for Singular Boundary Value Problems on the Infinite Interval Ke Wang, Ying Wang* School of Mathematics and Statistics, Linyi University, Linyi Shandong th th nd Received: Nov. 30 , 2017; accepted: Dec. 15 , 2017; published: Dec. 22 , 2017 Abstract The theory of differential equations in Banach spaces is an important branch of nonlinear analy- sis. The boundary value problem of differential equation is the component of the differential equ- ation 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 vi- bration, 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 posi- tive solutions for a class of boundary value problems of differential equation on the infinite inter- val 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. Keywords Positive Solutions, Cone, Fixed Points, Infinite Interval 无穷区间上奇异边值问题正解的存在性 王 克，王 颖* 临沂大学数学与统计学院，山东 临沂 收稿日期：2017年11月30 日；录用日期：2017年12月15 日；发布日期：2017年12月22 日 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 *通讯作者。 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. DOI: 10.12677/aam.2017.69140 王克，王颖 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