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Article type: Research Article
Authors: Agarwal, Ravi P. | O'Regan, Donal | Wong, Patricia J.Y.
Affiliations: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901‐6975, USA E‐mail: agarwal@fit.edu | Department of Mathematics, National University of Ireland, Galway, Ireland | School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore E‐mail: ejywong@ntu.edu.sg
Abstract: We consider the following system of integral equations ui(t)=μ∫01gi(t,s)f(s,u1(s),u2(s),…,un(s)) ds, t∈[0,1], 1≤i≤n, where μ>0, the function f may take negative values and f(·,u1,u2,…,un) may be singular at uj=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,∞) ui(t)=μ∫0∞gi(t,s)f(s,u1(s),u2(s),…,un(s)) ds, t∈[0,∞), 1≤i≤n.
Keywords: semipositone, system of singular integral equations, constant‐sign solutions, boundary value problems
Journal: Asymptotic Analysis, vol. 43, no. 1-2, pp. 47-74, 2005
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