Existence and regularity of solutions in alpha norm for some second order partial neutral functional differential equations in Banach spaces

Djendode Mbainadji; Al-hassem Nayam; Issa  Zabsonre

doi:10.26637/mjm1201/008

Abstract

The purpose of this paper is to study the existence and regularity of solutions in the $\alpha$-norm for some second order partial neutral functional differential equations with finite delay in Banach spaces. To do this, we use the cosine family theory and Schauder's fixed point Theorem to establish the local existence of solutions and we give some sufficients conditions to enssure the regularity of solutions. Finally, we give an example to illustrate the theoretical results.

Keywords:

Cosine family, Mild and strict solutions, Neutral equations, second order functional differential equations, $\alpha$ norm

Mathematics Subject Classification:

47D09, 34K40, 45N05, 35A01

Authors Imprint References Funding Related Articles Downloads

Djendode Mbainadji Université Polytechnique de Mongo, Département des sciences Fondamentales, B.P.4377, Mongo, Tchad.
Al-hassem Nayam Université de Ndjamena, Faculté des Sciences Exactes et Appliquées, chad
Issa Zabsonre Université Joseph KI-ZERBO, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Département de Mathématiques https://orcid.org/0000-0002-2968-8481

Pages: 104-121
Date Published: 01-01-2024
Vol. 12 No. 01 (2024): Malaya Journal of Matematik (MJM)

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