A promenade in the world of periodicity

Abstract

In this talk, we will present from the point of view of differential equations several concepts of periodicity and their generalizations motivated by some periodic phenomena. We will give an elementary proof of the celebrated Massera Theorem for periodic differential equations. We will prove also that under some appropriate conditions, a second-order semilinear elliptic almost periodic equation has no almost periodic solution (in the sense of Bohr), but many almost automorphic and almost periodic (in the sense of Besicovitch) solutions in the envelope of the equation. We apply the results to study an almost periodically forced pen.