First order functional differential equations with periodic boundary conditions

Abstract

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.

Keywords:

• Banach algebra
• Periodic boundary value problem
• Existence theorems
• Extremal solutions

Keywords:

• 2000 Mathematics Subject Classifications: 34K10

Acknowledgements

The research of J. R. Graef was supported in part by the Office of Academic and Research Computing Services of the University of Tennessee at Chattanooga.