Noncompact-type Krasnoselskii fixed-point theorems and their applications

被引：16

作者：

Xiang, Tian ^{[1
]}

Georgiev, Svetlin Georgiev ^{[2
]}

机构：

[1] Renmin Univ China, Inst Math Sci, Beijing 100872, Peoples R China

[2] Univ Sofia, Fac Math & Informat, Dept Differential Equat, BU-1126 Sofia, Bulgaria

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2016年 / 39卷 / 04期

基金：

中国博士后科学基金;

关键词：

transport equations; fixed point theorems; noncompact mappings; measure of noncompactness; contractions; expansions; integral equations; difference equations; SUM; SCHAUDER; EXISTENCE;

D O I：

10.1002/mma.3525

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first establish some user-friendly versions of fixed-point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed-point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed-point theorem. Next, with these obtained fixed-point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra-type integral equations. Copyright (c) 2015 John Wiley & Sons, Ltd.

引用

页码：833 / 863

页数：31

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