Positive solutions for a system of nonlinear singular Hammerstein integral equations via nonnegative matrices and applications

We are concerned with the existence and multiplicity of positive solutions for the system of nonlinear singular Hammerstein integral equations u(i)(t) = integral(b)(a)k(i)(t, s)g(i)(s)f(i)(s, u(1)(s),..., u(n)(s))ds, i = 1, 2,..., n. We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing nonnegative matrices. As applications, the main results are applied to establish the existence and multiplicity of positive solutions for an elliptic system in an annulus.