NONLINEAR QUADRATIC FIRST ORDER FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

In this paper, an existence theorem for the periodic boundary value problems of first order quadratic functional integro-differential equations is proved via a fixed point theorem in Banach algebras and under some mixed generalized Lipschitz and Carath´eodory conditions. The existence theorems for extremal positive solutions are also proved under certain monotonicity conditions.