The existence theorems of the random solutions for random Hammerstein type nonlinear integral equations
type: Item
instance of: scholarly article
title: The existence theorems of the random solutions for random Hammerstein type nonlinear integral equations
zbMATH Open document ID: 0957.45022
DOI: 10.1016/S0893-9659(00)00064-1
author: Guozhen Li
author: Lokenath Debnath
published in: Applied Mathematics Letters
publication date: 2000-11-16T00:00:00Z
review text: Under certain conditions, existence of a nonnegative, not identically vanishing, random continuous solution \(\varphi (\omega,x)\) is proved for the random nonlinear Hammerstein integral equation \[ \varphi= \int_G k(\omega,x, y)f(y,\varphi) dy \] where \(f(x,u)= \sum^n_{i=1} a_i(x) u^{a_i}\), \(a_i>0\), \(a_i(x)\geq 0\), and \(G\) is a bounded closed domain in \(R^N\).
Mathematics Subject Classification ID: 45R05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 1531189
zbMATH Keywords: positive solution
zbMATH Keywords: existence
zbMATH Keywords: random continuous solution
zbMATH Keywords: random nonlinear Hammerstein integral equation
reviewed by: Melvin D. Lax
MaRDI profile type: Publication
cites work: Q3336252
cites work: Random integral equations
cites work: Q5812325
full work available at URL: s0893-9659(00)00064-1
OpenAlex ID: W2066165807
description: scientific article; zbMATH DE number 1531189