Cubo (Dec 2021)

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

  • Abdelhai Elazzouzi,
  • Khalil Ezzinbi,
  • Mohammed Kriche

DOI
https://doi.org/10.4067/S0719-06462021000300469
Journal volume & issue
Vol. 23, no. 3
pp. 469 – 487

Abstract

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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.

Keywords