SOLUTIONS FOR SINGULAR VOLTERRA INTEGRAL EQUATIONS

We consider the system of Volterra integral equations u(i)(t) = integral(t)(0) gi(t, s)[Pi(s, u(1)(s), u2(s), ..., u(n)(s)) + Q(i)(s, u(1)(s), u(2)(s), ..., u(n)(s))]ds, t is an element of [0, T], 1 <= i <= n where T > 0 is fixed and the nonlinearities P-i(t, u(1), u(2), ..., u(n)) can be singular at t = 0 and u(j) = 0 where j is an element of {1, 2, ..., n}. Criteria are offered for the existence of fixed-sign solutions (u(1)*, u(2)*, ..., u(n)*) to the system of Volterra integral equations, i.e., theta(i)u(i)*(t) >= 0 for t is an element of [0, 1] and 1 <= i <= n, where theta(i) is an element of {1, -1} is fixed. We also include an example to illustrate the usefulness of the results obtained.