Monotone method for integrodifferential equation with periodic boundary conditions

Abstract

Consider the integrodifferential equation with periodic boundary conditions. By developing the compari- son results relative to PBVP for integrodifferential equations and using a fixed point theorem of nonlinear opera- tors whose domain and range are different, we develop the monotone method. Consequently, we prove the existence of extremal solutions of the PBVP of the integrodifferential equation