一类分数阶差分方程边值问题递增正解的存在性

J4 ›› 2013, Vol. 51 ›› Issue (01): 47-52.

一类分数阶差分方程边值问题递增正解的存在性

葛琦, 侯成敏

延边大学理学院数学系, 吉林延吉 133002

收稿日期:2012-06-07 出版日期:2013-01-26 发布日期:2013-01-31
通讯作者: 葛琦 E-mail:geqi9688@163.com

Existence of Positive and Nondecreasing Solution of BoundaryValue Problems for a Class of Fractional Difference Equations

GE Qi, HOU Chengmin

Department of Mathematics, College of Science, Yanbian University, Yanji 133002, Jilin Province, China

Received:2012-06-07 Online:2013-01-26 Published:2013-01-31
Contact: GE Qi E-mail:geqi9688@163.com

摘要/Abstract

摘要：

在度量空间中利用不动点定理, 研究一类带有分数阶边界条件的分数阶差分方程递增正解的存在性. 借助Green函数的性质, 分别建立了该方程存在唯一递增非负解的充分条件及存在唯一严格递增正解的充分条件.

关键词: 分数阶边界条件； Green函数；严格递增

Abstract:

Using fixed point theorem in metric space, the authors studied the existence of positive and nondecreasing solution for a class of the fractional difference equations with fractional boundary conditions. With the aid of some characteristics of the Green’s function, we obtained sufficient conditions for the existence of a unique nonnegative and nondecreasing solution to this class of equations. And we discussed the existence and uniqueness of a positive and strictly increasing solution to this equations.

Key words: fractional boundary conditions, Green’s function, strictly increasing

中图分类号:

O175.7

葛琦, 侯成敏. 一类分数阶差分方程边值问题递增正解的存在性[J]. J4, 2013, 51(01): 47-52.

GE Qi, HOU Cheng-Min. Existence of Positive and Nondecreasing Solution of BoundaryValue Problems for a Class of Fractional Difference Equations[J]. J4, 2013, 51(01): 47-52.