Massera problem for non-autonomous retarded differential equations

Zitane, Mohamed; Bensouda, Charaf

doi:10.1016/j.jmaa.2013.01.046

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Its applications in the life sciences range from simple predator-prey models to complicated signal traduction pathways in biological cells, in physics from the motion of a pendulum to complex climate models, and beyond that to further fields as diverse as chemistry (reaction kinetics), economics, engineering, sociology, demography, and biosciences. Nonautonomous differential equations has received the great attention see for instance the works [22,26,28,40,42,47,51] and some recent works [9,[37][38][39]. For some applications, we refer the reader to the handbook by Peter E. Kloeden and Christian Pötzsche [44].…”

Section: Introductionmentioning

confidence: 99%

Existence results on nonautonomous partial functional differential equations with state-dependent infinite delay

2023

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The aim of this work is to establish the existence of mild solutions for some nondensely nonau-tonomous partial functional differential equations with state-dependent infinite delay in Banachspace. We assume that, the linear part is not necessarily densely defined and generates an evolution family under the hyperbolique conditions. We use the classic Shauder Fixed Point Theorem, the Nonlinear Alternative Leray-Schauder Fixed Point Theorem and the theory of evolution family, we show the existence of mild solutions. Secondly, we obtain the existence of mild solution in a maximal interval using Banach’s Fixed Point Theorem which may blow up at the finite time, weshow that this solution depends continuously on the initial data under the global Lipschitz condition on the second argument of F and we get the existence of global mild solution. We proposesome model arising in dynamic population for the application of our results.

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Section: Introductionmentioning

confidence: 99%

Existence results on nonautonomous partial functional differential equations with state-dependent infinite delay

2023

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“…2 But this does not hold for linear almost periodic systems in the absence of Favard's separability. [3][4][5] For some new developments, one can see previous studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and references therein. In the last decades, a great deal of attention has been paid to study the spatio-temporal patterns, e.g., rotating spiral waves.…”

Section: Introductionmentioning

confidence: 99%

Affine‐periodic orbits for linear dynamical systems

Yang

Cheng

2022

Math Methods in App Sciences

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We observe the relationship between forward bounded orbits and affine periodic orbits for infinite‐dimensional linear dynamical systems and prove a Massera type criterion, which asserts that a forward bounded orbit implies the existence of affine periodic orbits. Such an affine‐periodic orbit might be periodic, quasi(almost)‐periodic, or spiral one. We also give an analog for hybrid (switching) discrete dynamical systems.

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Periodic Solutions for Non-Autonomous Neutral Functional Differential Equations with Finite Delay

Zitane

2017

Acta Math Vietnam

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Massera problem for non-autonomous retarded differential equations

Cited by 6 publications

References 14 publications

Existence results on nonautonomous partial functional differential equations with state-dependent infinite delay

Existence results on nonautonomous partial functional differential equations with state-dependent infinite delay

Affine‐periodic orbits for linear dynamical systems

Periodic Solutions for Non-Autonomous Neutral Functional Differential Equations with Finite Delay

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