On the periodic solutions for some retarded partial differential equations by the use of semi-Fredholm operators

  • Abdelhai Elazzouzi Département de Mathématiques, Laboratoire des Sciences de l’Ingénieur (LSI), Faculté Polydisciplinaire de Taza, Université Sidi Mohamed Ben Abdellah (USMBA) - Fes, BP. 1223, Taza, Morocco.
  • Khalil Ezzinbi Département de Mathématiques, Laboratoire des Sciences de l’Ingénieur (LSI), Faculté Polydisciplinaire de Taza, Université Sidi Mohamed Ben Abdellah (USMBA) - Fes, BP. 1223, Taza, Morocco – Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakesh, Morocco.
  • Mohammed Kriche Département de Mathématiques, Laboratoire des Sciences de l’Ingénieur (LSI), Faculté Polydisciplinaire de Taza, Université Sidi Mohamed Ben Abdellah (USMBA) - Fes, BP. 1223, Taza, Morocco.
Keywords: Hille-Yosida condition, Integral solutions, Semigroup, Semi-Fredholm operators, Periodic solution, Poincaré map

Abstract

The main goal of this work is to examine the periodic dynamic behavior of some retarded periodic partial differential equations (PDE). Taking into consideration that the linear part realizes the Hille-Yosida condition, we discuss the Massera’s problem to this class of equations. Especially, we use the perturbation theory of semi-Fredholm operators and the Chow and Hale’s fixed point theorem to study the relation between the boundedness and the periodicity of solutions for some inhomogeneous linear retarded PDE. An example is also given at the end of this work to show the applicability of our theoretical results.

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Published
2021-12-01
How to Cite
[1]
A. Elazzouzi, K. Ezzinbi, and M. Kriche, “On the periodic solutions for some retarded partial differential equations by the use of semi-Fredholm operators”, CUBO, vol. 23, no. 3, pp. 469–487, Dec. 2021.
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Articles