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Constant-sign solutions of a system of integral equations: The semipositone and singular case

Constant-sign solutions of a system of integral equations: The semipositone and singular case We consider the following system of integral equations u i (t)=μ∫ 0 1 g i (t,s)f(s,u 1 (s),u 2 (s),…,u n (s)) ds, t∈(0,1), 1≤i≤n, where μ>0, the function f may take negative values and f(·,u 1 ,u 2 ,…,u n ) may be singular at u j =0, j∈{1,2,…,n}. Our aim is to establish criteria such that the above system has a constant-sign solution. To illustrate the generality of the results obtained, application to a well known boundary value problem is included. We also extend the above problem to that on the half-line (0,∞) u i (t)=μ∫ 0 ∞ g i (t,s)f(s,u 1 (s),u 2 (s),…,u n (s)) ds, t∈(0,∞), 1≤i≤n. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Asymptotic Analysis IOS Press

Constant-sign solutions of a system of integral equations: The semipositone and singular case

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Publisher
IOS Press
Copyright
Copyright © 2005 by IOS Press, Inc
ISSN
0921-7134
eISSN
1875-8576
Publisher site
See Article on Publisher Site

Abstract

We consider the following system of integral equations u i (t)=μ∫ 0 1 g i (t,s)f(s,u 1 (s),u 2 (s),…,u n (s)) ds, t∈(0,1), 1≤i≤n, where μ>0, the function f may take negative values and f(·,u 1 ,u 2 ,…,u n ) may be singular at u j =0, j∈{1,2,…,n}. Our aim is to establish criteria such that the above system has a constant-sign solution. To illustrate the generality of the results obtained, application to a well known boundary value problem is included. We also extend the above problem to that on the half-line (0,∞) u i (t)=μ∫ 0 ∞ g i (t,s)f(s,u 1 (s),u 2 (s),…,u n (s)) ds, t∈(0,∞), 1≤i≤n.

Journal

Asymptotic AnalysisIOS Press

Published: Jan 1, 2005

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