Nonlinear Volterra equation with nondecreasing kernel
type: Item
instance of: scholarly article
title: Nonlinear Volterra equation with nondecreasing kernel
zbMATH Open document ID: 0851.45004
author: Z. B. Tsalyuk
published in: Russian Mathematics
publication date: 1996-08-21T00:00:00Z
review text: The author considers the following system of integral equations \[ x(t)= \int^t_0 k(t, s, x(s)) ds+ f(t), \qquad t\geq 0, \tag{1} \] where all functions are continuous in their domains and the kernel \(K(t, s, x)\) is a nondecreasing function of \(x\in \mathbb{R}^n\) (componentwise). By means of methods connected with integral inequalities existence and uniqueness theorems are proved for equation (1) and certain of its special cases.
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 898884
zbMATH Keywords: nonlinear Volterra equation
zbMATH Keywords: successive approximations
zbMATH Keywords: system of integral equations
zbMATH Keywords: integral inequalities
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 898884