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

Moussa El-Khalil Kpoumié; Abdel Hamid Gamal  NSANGOU; Patrice NDAMBOMVE

doi:10.26637/mjm1103/001

Abstract

The aim of this work is to establish the existence of mild solutions for some nondensely nonautonomous partial functional differential equations with state-dependent infinite delay in Banach space. 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, we show 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.

Keywords:

Nondensely nonautonomous equations, evolution family, hyperbolique conditions, mild solutions, state-dependent infinite delay

Mathematics Subject Classification:

34K43, 35R10, 47J35

Authors Imprint References Funding Related Articles Downloads

Moussa El-Khalil Kpoumié Université de Ngaoundéré, ´ Ecole de Géologie et Exploitation Minière, Département de Mathématiques Appliquées et Informatique, B.P. 115 Meiganga, Cameroun.
Abdel Hamid Gamal NSANGOU Université de Maroua, ´ Ecole Nationle supérieure polytechnique de Maroua, Département enseignements scientifiques de base, B.P. 46 Maroua, Cameroun.
Patrice NDAMBOMVE University of Buea, Faculty of Science, Departement of Mathematics, P.O. Box 63, Cameroon.

Pages: 239-262
Date Published: 01-07-2023
Vol. 11 No. 03 (2023): Malaya Journal of Matematik (MJM)

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