Periodic Solution for some Class of Linear Partial Differential Equation with infinite Delay using Semi-Fredholm perturbations

Author:

Elazzouzi Abdelhai1,Ezzinbi Khalil2,Kriche Mohammed1

Affiliation:

1. Université Sidi Mohamed Ben Abdellah-USMBA , Faculté Polydisciplinaire de Taza Département de Mathématiques , BP. 1223, Taza , Morocco Laboratoire des Sciences de l’Ingénieur – LSI

2. Université Cadi Ayyad , Faculté des Sciences Semlalia, Département de Mathématiques , B.P. 2390, Marrakesh , Morocco

Abstract

Abstract In this work, we study the existence of periodic solutions for a class of linear partial functional differential equations with infinite delay. Inspiring by an existing study, by applying the perturbation theory of semi-Fredholm operators, we introduce a suitable a priori estimate on the norm of the operator L to establish the periodicity of solutions in the case where the linear part is nondensely defined and satisfies the Hille-Yosida condition and without considering the exponential stability condition on the semigroup generated by the part of this operator on the closure of it’s domain. Moreover, in the special case where the linear part generates a strongly continuous semigroup and perturbed by a compact linear operator, we give some sufficient conditions to derive periodic solution from bounded ones. Finally, our theoretical results are illustrated by applications in both densely and nondensely cases.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Statistics and Probability,Analysis

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