PERIODIC BOUNDARY VALUE PROBLEMS OF FIRST ORDER ORDINARY CARATHEODORY AND DISCONTINUOUS DIFFERNTIAL EQUATIONS

Abstract

In this paper, an existence theorem for the periodic boundary value problems of first order Carathe ́eodory and discontinuous differential equations is proved in Banach algebras under the mixed generalized Lipschitz and Carathéodory conditions. The existence theorems for extremal solutions are also proved under certain monotonicity conditions.