Pseudo almost periodic solutions for some differential equations in a banach space

Dads, E. Ait; Ezzinbi, Khalil; Arino, Ovide

doi:10.1016/s0362-546x(97)82865-9

Cited by 84 publications

(4 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are a lot of work on this theme (see ). In this article, we consider a more general setting and use slightly different techniques to study the existence of pseudo almost periodic solutions under the measure theory to the class of abstract nonautonomous differential equations

\frac{d}{d t} 1.19em [u (t) + F (t, B (t) u (t)) 1.19em] = A (t) u (t) + G (t, C (t) u (t)), t \in double-struckR,

where A ( t ) for

t \in double-struckR

is a family of closed linear operators on D ( A ( t )) satisfying the well‐known Acquistapace‐Terreni conditions, B ( t ), C ( t ) (

t \in double-struckR

) are families of (possibly unbounded) linear operators, and

F : double-struckR \times double-struckX \mapsto {double-struckX}_{β}^{t}, G : double-struckR \times double-struckX \mapsto double-struckX

are μ ‐pseudo almost periodic in

t \in double-struckR

uniformly in the second variable.…”

Section: Introductionmentioning

confidence: 99%

Existence ofμ−pseudo almost periodic solutions to some evolution equations

Miraoui

2017

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

In this article, a new approach for pseudo almost periodic solution under the measure theory, under Acquistpace‐Terreni conditions. We make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of μ‐pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations. For illustration, we propose some application to a nonautonomous heat equation. Copyright © 2017 John Wiley & Sons, Ltd.

show abstract

\frac{d}{d t} 1.19em [u (t) + F (t, B (t) u (t)) 1.19em] = A (t) u (t) + G (t, C (t) u (t)), t \in double-struckR,

where A ( t ) for

t \in double-struckR

is a family of closed linear operators on D ( A ( t )) satisfying the well‐known Acquistapace‐Terreni conditions, B ( t ), C ( t ) (

t \in double-struckR

) are families of (possibly unbounded) linear operators, and

F : double-struckR \times double-struckX \mapsto {double-struckX}_{β}^{t}, G : double-struckR \times double-struckX \mapsto double-struckX

are μ ‐pseudo almost periodic in

t \in double-struckR

uniformly in the second variable.…”

Section: Introductionmentioning

confidence: 99%

Existence ofμ−pseudo almost periodic solutions to some evolution equations

Miraoui

2017

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

show abstract

“…In [?zhang], Zhang introduced an extension of the almost periodic functions, the so‐called pseudo almost periodic functions. This class of functions and some of its generalizations attracted the attention of many researchers because of its applications in the theory of differential equations; we refer to , ?cuevas_pinto]. The concept of weighted pseudo almost periodic functions was introduced by Diagana in as a generalization of pseudo almost periodicity.…”

Section: Introductionmentioning

confidence: 99%

Stepanov ergodic perturbations for some neutral partial functional differential equations

Es-sebbar

Ezzinbi

2015

Math Methods in App Sciences

View full text Add to dashboard Cite

In this work, we give sufficient conditions for the existence and uniqueness of pseudo almost periodic integral solutions for some neutral partial functional differential equations with Stepanov pseudo almost periodic forcing functions. Our working tools are based on the variation of constant formula and the spectral decomposition of the phase space. To illustrate our main results, we give applications to a neutral model arising in physical systems, as well as an application to heat equations with discrete and continuous delay.

show abstract

“…In addition, after considering longterm dynamical behaviour, it has been found that the investigation of almost periodic and pseudo almost periodic behaviour are in more accordance with reality since there is no phenomenon which is purely periodic. Hence, in the past two decades, some works dealing with the existence of almost periodic and/or pseudo almost periodic solutions of nonlinear differential equations have appeared with applications in different fields such as mathematical biology, control and physics ( [1,6,7,12,13,15,18,22] and the references therein).…”

Section: Introductionmentioning

confidence: 99%