First order functional differential equations with periodic boundary conditions - Dhage, B. C.; Graef, John R. (Applicable analysis, 2007)
In this article, the authors prove an existence theorem for periodic boundary value problems for first order functional differential equations (FDE) in Banach algebras under mixed generalized Lipschitz and Carathéodory conditions. The existence of extremal positive solutions is also proved under certain monotonicity conditions. An example illustrating the results is included.