Globally Exponential Stability of Piecewise Pseudo Almost Periodic Solutions for Neutral Differential Equations with Impulses and Delays

He, Jianxin; Kong, Fanchao; Nieto, Juan J.; Qiu, Hongjun

doi:10.1007/s12346-022-00578-x

Cited by 5 publications

(1 citation statement)

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“…The study of a.p. (and its extensions) solution to this kind of equations has been under examination by several researchers over last decades, we refer the reader to previous works [29][30][31][32] and the references therein. Nevertheless, there is no work in the literature that deals with this type of equation in E-w.a.p.…”

Section: Introductionmentioning

confidence: 99%

Stepanov Eberlein almost periodic functions and applications

Ait Dads,

Fatajou,

Zizi

2023

Math Methods in App Sciences

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In this paper, we prove that the class of Eberlein weakly almost periodic functions in the Stepanov's sense is strictly larger than both Eberlein weak almost periodicity (E‐w.a.p.) and Stepanov's almost periodicity. Some examples are provided. We present a composition result for this class of functions, and using Banach fixed‐point theorem, we prove the existence and uniqueness of E‐w.a.p. solution for a differential equation of neutral type with nondense domain when the forcing terms are only E‐w.a.p. in the Stepanov's sense. We mention that our results can extend and improve previous several works in this direction. An application is given to illustrate the result.

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Section: Introductionmentioning

confidence: 99%

Stepanov Eberlein almost periodic functions and applications

Ait Dads,

Fatajou,

Zizi

2023

Math Methods in App Sciences

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Existence and exponential stability of the piecewise pseudo almost periodic mild solution for some partial impulsive stochastic neutral evolution equations

Miraoui

Missaoui

2023

Math Methods in App Sciences

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In the present paper, we first introduce the concept of double measure ‐mean piecewise pseudo almost periodic for stochastic processes for . Next, we make extensive use of the exponential dichotomy techniques and a fixed point strategy with stochastic analysis theory to obtain the existence of doubly measure ‐mean piecewise pseudo almost periodic mild solutions for a class of impulsive non‐autonomous partial stochastic evolution equations in Hilbert spaces. In addition, we study the exponential stability of ‐mean piecewise pseudo almost periodic mild solutions. Finally, we give an example to confirm the reliability and feasibility of our findings.

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