A method for studying integral equations by using a covering set of the Nemytskii operator in spaces of measurable functions
type: Item
instance of: scholarly article
title: A method for studying integral equations by using a covering set of the Nemytskii operator in spaces of measurable functions
zbMATH Open document ID: 1491.45009
DOI: 10.1134/S0012266122010104
author: W. Merchela
author: E. S. Zhukovskiy
published in: Differential Equations
publication date: 2022-03-22T00:00:00Z
review text: The authors present some existence results for the scalar nonlinear Fredholm equation \[ f\left(t,\int_0^1 K(t,s)x(s)ds,x(t)\right)=z(t), \] and for the Volterra integral equation \[ f\left(t,\int_0^t K(t,s)x(s)ds,x(t)\right)=z(t),\] with \(t\in[0,1] \) by using the method of covering sets of Nemytskii operators.
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7495303
zbMATH Keywords: existence of solutions
zbMATH Keywords: covering mappings
zbMATH Keywords: nonlinear Fredholm and Volterra operators
reviewed by: Leonid Berezansky
MaRDI profile type: Publication
Wikidata QID: Q115249023
cites work: Covering mappings and well-posedness of nonlinear Volterra equations
cites work: Covering mappings and their applications to differential equations unsolved for the derivative
cites work: On the well-posedness of differential equations unsolved for the derivative
cites work: Covering mappings in a product of metric spaces and boundary value problems for differential equations unsolved for the derivative
cites work: Second order necessary conditions for optimal impulsive control problems
cites work: Theory of \((q_1,q_2)\)-quasimetric spaces and coincidence points
cites work: $ (q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points
cites work: On covering mappings in generalized metric spaces in studying implicit differential equations
cites work: Q5544938
cites work: Volterra integral equations
cites work: Q4275439
cites work: Integral equations of the third kind in \(L^p\) spaces
cites work: Covering mappings in metric spaces and fixed points
cites work: On order covering maps in ordered spaces and Chaplygin-type inequalities
cites work: Q4044371
cites work: Q3114392
cites work: Volterra inequalities in function spaces
description: scientific article; zbMATH DE number 7495303