无穷区间上二阶三点差分方程边值问题正解的存在性  

Existence of positive solutions to boundary value problem of second-order three-point difference equations on infinite intervals

作　　者：郭彦平[1] 苗素荣 禹长龙[1] 

机构地区：[1]河北科技大学理学院,河北石家庄050018

出　　处：《河北科技大学学报》2016年第6期556-561,共6页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(11201112);河北省自然科学基金(A2013208147;A2014208152;A2015208114);河北省高等学校科学技术研究项目(QN2015175;QN2016165)

摘　　要：为了将差分方程应用到解无穷区间边值问题,借助于相应线性边值问题Green函数的性质,研究了无穷区间上的二阶三点差分方程边值问题。通过Banach压缩映像原理和LeraySchauder不动点定理获得了该问题正解的存在性和唯一性定理,推广了已有结论。In order to apply difference equation in boundary value problem on infinite intervals, with the help of the properties of Green function in linear boundary value problems, the boundary value problem of second-order three-point difference equations on infinite intervals is studied. The theory of existence and uniqueness of positive solutions to this problem is are obtained by Banach ＇ s contraction mapping principle and Leray-Schauder fixed point theorem, which generalizes the known results.

关 键 词：常微分方程其他学科 差分方程 GREEN函数 LERAY-SCHAUDER不动点定理 无穷区间 

分 类 号：O175[理学—数学]