Existence of solutions for some nonautonomous partial functional differential equations with state-dependent delay

Kpoumiè, Moussa El-Khalil; Nsangou, Abdel Hamid Gamal; Ndambomve, Patrice; Zabsonre, Issa; Mboutngam, Salifou

doi:10.1007/s40324-019-00206-w

Cited by 2 publications

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References 27 publications

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“…We point out that the work of this paper is the following of [5,7,12,15]. But under appropriate circonstances, evolutionary families are not compact.…”

Section: Introductionmentioning

confidence: 98%

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Mild solutions for some nonautonomous evolution equations with state-dependent delay governed by equicontinuous evolution families

Kpoumié,

Djeunankam,

Mbang

et al. 2023

Malaya J. Mat.

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In this work, we study the existence solutions and the dependence continuous with the initial data for some nondensely nonautonomous partial functional differential equations with state-dependent delay in Banach spaces. We assume that the linear part is not necessarily densely defined, satisfies the well-known hyperbolic conditions and generate a noncompact evolution family. Our existence results are based on Sadovskii fixed point Theorem. An application is provided to a reaction-diffusion equation with state-dependent delay.

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“…We point out that the work of this paper is the following of [5,7,12,15]. But under appropriate circonstances, evolutionary families are not compact.…”

Section: Introductionmentioning

confidence: 98%

“…In 2019, Kpoumie et al investigated in [15] several results on the existence of solutions of the following nonautomous equations:…”

Section: Introductionmentioning

confidence: 99%

Mild solutions for some nonautonomous evolution equations with state-dependent delay governed by equicontinuous evolution families

Kpoumié,

Djeunankam,

Mbang

et al. 2023

Malaya J. Mat.

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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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Existence of solutions for some nonautonomous partial functional differential equations with state-dependent delay

Cited by 2 publications

References 27 publications

Mild solutions for some nonautonomous evolution equations with state-dependent delay governed by equicontinuous evolution families

Mild solutions for some nonautonomous evolution equations with state-dependent delay governed by equicontinuous evolution families

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

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