Abstract
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.
Highlights
The theory of uniformly almost periodic functions was introduced and studied by H
The concept of (w, c) −almost periodicity introduced in [10] is a generalization of (w, c) −periodicity which motivated by some known results regarding the qualitative properties of solutions to the Mathieu linear second-order di erential equation y′′ (t) + [a − q cos t] y (t) =, arising in seasonally forced population dynamics, see [1]
Zhang introduced an extension of the almost periodic functions, the so-called pseudo almost periodic functions. These pseudo almost periodic functions are related to many applications in the theory of di erential equations
Summary
The theory of uniformly almost periodic functions was introduced and studied by H. The paper [12] introduce and investigate the (w, c) −almost periodicity in the setting of Sobolev-Schwartz distributions. As mentioned in the abstract, the main aim of this paper is to introduce a new space of (w, c)−pseudo almost periodic distributions containing (w, c)−pseudo almost periodic functions as well as (w, c)−almost periodic Schwartz distributions. The paper is brie y described as follows: In section , we recall the basic de nitions and results of the concept of (w, c)−pseudo almost periodic functions. We introduce and study the (w, c)−pseudo almost periodicity in the setting of Sobolev-Schwartz distributions, by recalling some new basic spaces of functions and distributions in which we can study this concept of (w, c)−pseudo almost periodicity. We recall the space APw,c of (w, c)− almost periodic functions which has been introduced in [10].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
