Positive periodic solutions of second-order differential equations with weak singularities

where a, c : Z ® R+ are T-periodic functions, f Î C(Z × (0, ∞), R) is T-periodic with respect to t and singular at u = 0. Positive periodic solutions of second-order difference equations have been studied by many authors, see [1-6]. However, in these therein, the nonlinearities are nonsingular, what would happen if the nonlinearity term is singular? It is of interest to note here that singular boundary value problems in the continuous case have been studied in great detail in the literature [7-20]. In 1987, Lazer and Solimini [7] firstly investigated the existence of the positive periodic solutions of the problem