Compactness conditions in the study of functional, differential, and integral equations
type: Item
instance of: scholarly article
title: Compactness conditions in the study of functional, differential, and integral equations
zbMATH Open document ID: 1266.45008
DOI: 10.1155/2013/819315
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: We discuss some existence results for various types of functional, differential, and integral equations which can be obtained with the help of argumentations based on compactness conditions. We restrict ourselves to some classical compactness conditions appearing in fixed point theorems due to Schauder, Krasnosel'skii-Burton, and Schaefer. We present also the technique associated with measures of noncompactness and we illustrate its applicability in proving the solvability of some functional integral equations. Apart from this, we discuss the application of the mentioned technique to the theory of ordinary differential equations in Banach spaces.
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 6161380
zbMATH Keywords: compactness conditions
zbMATH Keywords: measures of noncompactness
zbMATH Keywords: functional integral equations
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: Banach spaces
Wikidata QID: Q58917539
author: Józef Banaś
author: K. Sadarangani
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/819315
OpenAlex ID: W2068656662
cites work: Q5522002
cites work: Q5185568
cites work: Q4340161
cites work: Q4340096
cites work: Fixed point theory and applications
cites work: Q4421936
cites work: Measures of noncompactness and condensing operators. Transl. from the Russian by A. Iacob
cites work: Q4040886
cites work: Q3883053
cites work: Q3862642
cites work: Measures of noncompactness in the study of solutions of nonlinear differential and integral equations
cites work: Q3997912
cites work: Q3258005
cites work: Q4045174
cites work: An existence theorem for nonlinear Volterra integral equation with deviating argument
cites work: Q3847203
cites work: Schaefer-Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
cites work: A fixed-point theorem of Krasnoselskii
cites work: Existence and global attractivity of solutions of a nonlinear functional integral equation
cites work: An application of a measure of noncompactness in the study of asymptotic stability
cites work: The global attractivity and asymptotic stability of solution of a nonlinear integral equation
cites work: Über die Methode der a priori-Schranken
cites work: A Fixed Point Theorem of Krasnoselskii—Schaefer Type
cites work: On existence and asymptotic behaviour of solutions of a functional integral equation
cites work: Q4048102
cites work: Existence of solutions for a class of nonlinear Volterra singular integral equations
cites work: Q3967843
cites work: Q3341199
cites work: Q3756045
cites work: Q5795253
cites work: Q5719637
cites work: Q5561202
cites work: Q3269329
cites work: Ordinary differential equations in Banach spaces
cites work: Q5665539
cites work: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach
cites work: Q4139053
cites work: Q5601071
cites work: Q5622727
cites work: On existence theorems for differential equations in Banach spaces
cites work: Solvability of infinite systems of differential equations in Banach sequence spaces
cites work: Applications of measures of noncompactness to the infinite system of differential equations in \(\ell_p\) spaces
cites work: Infinite system of differential equations in some \(BK\) spaces
description: scientific article; zbMATH DE number 6161380