Pseudo Almost Periodic Solutions of Some Delay Differential Equations

Dads, E. Ait; Ezzinbi, Khalil

doi:10.1006/jmaa.1996.0287

Cited by 42 publications

(8 citation statements)

References 5 publications

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“…As pointed out by E. Ait Dads and K. Ezzinbi in , it would be of great interest to study the dynamics of pseudo almost periodic systems with time delay. In addition, in view of the fact that many Nicholson's blowflies models display sustained fluctuations, it is thus desirable to construct Nicholson's blowflies models capable of producing pseudo almost periodic solution.…”

Section: Introductionmentioning

confidence: 99%

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

Duan

Huang

2014

Math. Meth. Appl. Sci.

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In this paper, we investigate a class of delay Nicholson's blowflies model with a linear harvesting term, new criteria for the existence and convergence dynamics of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic function, together with constructing suitable Lyapunov functionals. The obtained results extend previously known results, and they also partially answer an open problem proposed by L. Berezansky et al. Finally, an example with simulation is presented to demonstrate the effectiveness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

Duan

Huang

2014

Math. Meth. Appl. Sci.

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“…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.

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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.

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“…For every

t \in double-struckR

, the history function u t ∈ C is defined by

u_{t} (θ) : = u (t + θ), for θ \in [- r, 0] .

The existence of almost periodic solutions for differential equations has been extensively studied in the last 40 years. We specially mention the works of . In the literature, several books are devoted to cover this topic.…”

Section: Introductionmentioning

confidence: 99%

Behavior of bounded solutions for some almost periodic neutral partial functional differential equations

Dads

Es-sebbar

Ezzinbi

et al. 2016

Math Methods in App Sciences

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We establish a Bochner type characterization for Stepanov almost periodic functions, and we prove a new result about the integration of almost periodic functions. This result is then used together with a reduction principle to investigate the nature of bounded solutions of some almost periodic partial neutral functional differential equations. More specifically, we prove that all bounded solutions on double-struckR are almost periodic. Copyright © 2016 John Wiley & Sons, Ltd.

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Pseudo Almost Periodic Solutions of Some Delay Differential Equations

Cited by 42 publications

References 5 publications

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

Existence ofμ−pseudo almost periodic solutions to some evolution equations

Behavior of bounded solutions for some almost periodic neutral partial functional differential equations

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