Weakly almost periodic solutions of linear equations in Banach spaces

A Note on Almost Periodic Solutions of Semilinear Equations in Banach Spaces

In this article, we generalize the main result obtained by Bahaj in [1]. Also our proof is shorter than the original proof.

Periodic solutions for nonlinear Volterra integrodifferential equations in Banach spaces

In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we imp...

New Criteria for the Existence of Periodic and Almost Periodic Solutions for Some Evolution Equations in Banach Spaces

In this work we give a new criteria for the existence of periodic and almost periodic solutions for some differential equation in a Banach space. The linear part is nondensely defined and satisfies the Hille-Yosida condition. We prove the existence of periodic and almost periodic solutions with condition that is more general than the known exponential dichotomy. We apply the new criteria for th...

Almost periodic linear differential equations with non-separated solutions

A celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are non-separated (in a strong sense) sometimes al...

Existence of Periodic and Almost Periodic Solutions of Abstract Retarded Functional Difference Equations in Phase Spaces