Constant-sign solutions of a system of integral equations with integrable singularities

We consider the following systems of Fredholm integral equations and the system of Volterra integral equations where the nonlinearities fi, 1 ≤ i ≤ n may be singular in the independent variable and may also be singular at u_j = 0, j ∈ {1, 2,..., n}. Our aim is to establish criteria such that the above systems have at least one constant-sign solution (u1, u2,..., un), i.e., for each 1 ≤ i ≤ n, Θ_iu_i ≥ 0 where Θ_i ∈ {1,-1} is fixed.