Three positive solutions of a system of Fredholm integral equations.
type: Item
instance of: scholarly article
title: Three positive solutions of a system of Fredholm integral equations.
zbMATH Open document ID: 1067.45002
author: Ya-Hong Zhao
author: Jian-Ping Sun
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: For the system of Fredholm integral equations \[ u_i(t)= \int_0^1g_i(t,s)f_i\left(s,u_1(s),u_2(s),\dots,u_n(s)\right)\,ds,\quad t\in[0,1],\quad 1\leq i\leq n,\tag{1} \] the authors provide conditions on the nonlinearities \(f_i\) and kernels \(g_i\), so that the system (1) has at least three positive solutions. The main tool is the Leggett-Williams fixed-point theorem. The obtained results are applied to the system of second order Neumann boundary value problems \[ \begin{aligned} -u''_i(t)+c_iu_i(t)&=f_i(t,u_1(t),u_2(t),\dots,u_n(t)),\quad t\in[0,1],\\ u_i'(0)&=u_i'(1)=0,\quad 1\leq i\leq n,\\ \end{aligned} \] where \(c_i>0\) are fixed. Similarly, the results can be also applied to other well-known systems of boundary value problems, for example, \((m,p)\), Lidstone, focal, conjugate, Hermite and Sturm-Liouville, and extend the corresponding work in the literature.
reviewed by: Nikolay Yakovlevich Tikhonenko
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45M20
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 2140788
zbMATH Keywords: system of Fredholm integral equations
zbMATH Keywords: triple positive solutions
zbMATH Keywords: fixed-point theorem
zbMATH Keywords: system of Neumann boundary value problems
zbMATH Keywords: Lidstone boundary value problem
zbMATH Keywords: Hermite boundary value problem
zbMATH Keywords: focal boundary value problem
zbMATH Keywords: conjugate boundary value problem
zbMATH Keywords: Sturm-Liouville boundary value problem
MaRDI profile type: Publication
full work available at URL: j.aml.2004.07.014
OpenAlex ID: W2088667583
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DOI: 10.1016/J.AML.2004.07.014
description: scientific article; zbMATH DE number 2140788