(ω, c)- Pseudo almost periodic distributions

Abstract

The paper is a study of the (w, c) −pseudo almost periodicity in the setting of Sobolev-Schwartz distributions. We introduce the space of (w, c) −pseudo almost periodic distributions and give their principal properties. Some results about the existence of distributional (w, c) −pseudo almost periodic solutions of linear differential systems are proposed.

Existence of $$(N,\lambda )$$-Periodic Solutions for Abstract Fractional Difference Equations

“…In (1.1), A is a possibly unbounded operator defined on a Banach space X and f : Z × X → X is given. This class of (N, λ)-periodic functions was introduced in the reference [6] as the discrete counterpart of the notion of (ω, c)-periodic functions [10], a notion that has been studied by various authors, see, e.g., [8,9,[15][16][17][18][19]26] and [30]. It is worth noting that class of (N, λ)-periodic functions contains the classes of discrete periodic (λ = 1), discrete anti-periodic (λ = −1), discrete Bloch-periodic (λ = e ikN , k ∈ Z fixed), and unbounded functions.…”