J. Nonl. Evol. Equ. Appl. 2018 (5), pp. 57-74, published on August 26, 2019:

Pseudo almost periodic solutions for continuous algebraic difference equations

E. Ait Dads, L. Lhachimi

Cadi Ayyad University, Faculty of Sciences, Department of Mathematics, B.P. 2390 Marrakesh, Morocco

Received on November 10, 2016, revised version on January 26, 2017, by JNEEA in March 2018
Accepted on January 29, 2017

Communicated by Gaston M. N'Guerekata

Abstract.  Many phenomena in mathematical physics and in the theory of dynamical populations are described by difference equations. The aim of this work is to present new approach to study the qualitative properties of solutions for some algebraic difference equations. The technique used is based on convergence of series associated with the forcing term. We also consider the problem of existence of almost periodic solution by the compactly characterization of family associated with the forcing term. For illustration, we provide some applications. Our results generalizes the main results of our precedent work in [E.Ait Dads & L. Lhachimi, 2016].
Keywords:Bounded solution, Almost periodic - ergodic function, Pseudo almost periodic, Asymptotic behaviour, Kernels theorem decomposition, weak convergence, uniform convergence, simple convergence, greatest integer function..
2010 Mathematics Subject Classification:   39A13, 34C27.

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