The Generalized Solutions of One Order Periodic Boundary Value Problems in Banach Space

Abstract:

      In this paper, the authors study the periodic boundary value problems of a class of nonlinear integro-differential equations of mixed type in Banach space with Carath\'{e}odory's conditions. We arrive at the conclusion of the existence of generalized solutions between generalized upper and lower solutions, and develop the monotone iterative technique to find generalized extremal solutions as limits of monotone solution sequences in Banach space.