Integral equations with constraints and their solution methods
type: Item
instance of: scholarly article
title: Integral equations with constraints and their solution methods
zbMATH Open document ID: 0878.45002
DOI: 10.1007/BF02366501
author: A. Yu. Luchka
published in: Cybernetics and Systems Analysis
publication date: 1997-10-06T00:00:00Z
review text: Mathematical models of various physical phenomena and processes are described by integral equations, for instance \[ y(x)= f(x)+\int_\Omega F[x,t,y(t)]dt,\quad x\in\Omega\subset R^\ell,\tag{1} \] with additional information available about their solutions, in particular \[ \int_\Omega \Phi_s(t) y(t)dt=\alpha_s,\quad s=1,\dots,m,\tag{2} \] where \(f:\Omega\Rightarrow R\), \(F:\Omega\times\Omega\times R\Rightarrow R\) are given functions, \(y:\Omega\Rightarrow R\) is the sought function, and \(\Phi_s:\Omega\Rightarrow R\) and \(\alpha_s\in R\), \(s=1,\dots,m\), are a known system of linear independent functions and a known set of numbers. In general, problem (1) and (2) is inconsistent, but still it may be solvable for some initial values. We thus face the problem of establishing the conditions when equation (1) has a solution that satisfies the constraints (2) and developing methods to construct this solution.
Mathematics Subject Classification ID: 45G15
zbMATH DE Number: 1051095
zbMATH Keywords: inconsistent problems
zbMATH Keywords: nonlinear systems
zbMATH Keywords: integral equations with constraints
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1051095