Constant-sign solutions of a system of Fredholm integral equations

We consider the following system of Fredholm intergral equationsu(i)(t) = integral(0)(1) g(i)(t, s) f(i) (s, u(1)(s), u(2)(s),...,u(n)(s)) ds, t is an element of [0,1], 1 less than or equal to i less than or equal to n.Criteria are offered for the existence of single, double and multiple solutions of the system that are of constant signs. The generality of the results obtained is illustrated through applications to several well known boundary value problems. We also extend the above system of Fredholm intergral equations to that on the half-line [0, infinity]u(i)(t) = integral(0)(infinity) g(i)(t, s) f(i) (s, u(1)(s), u(2)(s),...,u(n)(s)) ds, t is an element of [0, 1], 1 less than or equal to i less than or equal to nand investigate the existence of constant-sign solutions.