On the solutions of a singular nonlinear periodic boundary value problem

In this paper, we consider the following singular nonlinear problem [GRAPHICS] where A is a positive continuous function on (0,1), q is a nonnegative measurable function on [0,1] and f is a nonnegative regular function on (0,1)x(0,infinity). We suppose that integral (1)(0)dt/A(t)< infinity and 0 < integral (1)(0)A(t)q(t) dt < infinity. Then we prove the existence and the uniqueness of a positive solution of this problem (P). Our approach is based on the use of the Green's function and the Schauder's fixed point theorem.