Constant-sign solutions for systems of singular integral equations of Hammerstein type

We consider the system of Hammerstein integral equations u(i)(t) = integral(T)(0) g(i)(t,s)f(i)(s, u(1)(s) + rho(1)(s), u(2)(s) + rho(2)(s), ..., u(n)(s) + rho(n)(s))ds, t is an element of [0, T], 1 <= i <= n where T > 0 is fixed, rho(i)'s are given functions and the nonlinearities f(i)(t, x(1), x(2), ..., x(n)) can be singular at t = 0 and x(j) = 0 where j is an element of {1, 2, ..., n}. Criteria are offered for the existence of constant-sign solutions, i.e., theta(i)u(i)(t) >= 0 for t is an element of [0, T] and 1 <= i <= n, where theta(i) is an element of {1, -1} g is fixed. The tools used are a nonlinear alternative of Leray-Schauder type, Krasnosel'skii's fixed point theorem in a cone and Schauder's fixed point theorem. We also include examples and applications to illustrate the usefulness of the results obtained. (C) 2009 Elsevier Ltd. All rights reserved.