Construction of measures of noncompactness of DCn[J, E] and C0n[J, E] with application to the solvability of nth-order integro-differential equations in Banach spaces

被引：0

作者：

Allahyari, Reza ^{[1
]}

Arab, Reza ^{[2
]}

Haghighi, Ali Shole ^{[2
]}

机构：

[1] Islamic Azad Univ, Mashhad Branch, Dept Math, Mashhad, Iran

[2] Islamic Azad Univ, Sari Branch, Dept Math, Sari, Iran

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2015年

关键词：

measure of noncompactness; Darbo fixed point theorem; Arzela-Ascoli theorem; nth-order integro-differential equations; INITIAL-VALUE PROBLEMS; INTEGRAL-DIFFERENTIAL EQUATIONS; ASYMPTOTIC STABILITY; MIXED-TYPE; GLOBAL-SOLUTIONS; SYSTEM; EXISTENCE;

D O I：

10.1186/s13662-015-0718-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we first investigate the construction of compact sets of DCn[J, E] and C-0(n)[J, E], and then we introduce new measures of noncompactness on these spaces. In addition, as an application, we discuss the existence of solutions of initial value problems for nth-order nonlinear integro-differential equations of mixed type on an infinite interval in Banach spaces. We will also state an interesting example which shows that our results can apply for solving infinite systems of integro-differential equations.

引用

页码：1 / 18

页数：18

共 8 条

[1] Existence of solutions for nth-order integro-differential equations in Banach spaces
Guo, DJ
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 41 (5-6) : 597 - 606
[2] Multiple positive solutions for nth-order impulsive integro-differential equations in Banach spaces
Guo, DJ
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (05) : 955 - 976
[3] Solutions for nth-order boundary value problems of impulsive singular nonlinear integro-differential equations in Banach spaces
Chen, Yanlai
Cao, Tingqiu
Qin, Baoxia
BOUNDARY VALUE PROBLEMS, 2014,
[4] Existence of positive solutions for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces
Guo, Dajun
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (09) : 2727 - 2740
[5] Construction of measures of noncompactness of DCn[J,E]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathit{DC}^{n}[J,E]$\end{document} and C0n[J,E]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C^{n}_{0}[J,E]$\end{document} with application to the solvability of nth-order integro-differential equations in Banach spaces
Reza Allahyari
Reza Arab
Ali Shole Haghighi
Advances in Difference Equations, 2015 (1)
[6] Positive solutions for nth-order nonlinear impulsive singular integro-differential equations on infinite intervals in Banach spaces
Zhang, Haijun
Liu, Lishan
Wu, Yonghong
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (02) : 772 - 787
[7] Positive solutions of an infinite boundary value problem for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces
Xu, Yumei
Zhang, Haijun
APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (09) : 5806 - 5818
[8] Positive solutions of an infinite boundary value problem for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces
Guo, Dajun
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (05) : 2078 - 2090

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