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

• Autores: Abdelhai Elazzouzi, Khalil Ezzinbi, Mohammed Kriche
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 23, Nº. 3, 2021, págs. 469-487
• Idioma: inglés
• DOI: 10.4067/S0719-06462021000300469
• Enlaces
  • Texto completo
• Resumen
  • español

    RESUMEN El principal objetivo de este trabajo es examinar el comportamiento dinámico periódico de algunas ecuaciones diferenciales parciales (EDP) periódicas con retardo. Tomando en consideración que la parte lineal cumple la condición de Hille-Yosida, discutimos el problema de Massera para esta clase de ecuaciones. Especialmente usamos la teoría de perturbaciones de operadores semi-Fredholm y el teorema de punto fijo de Chow y Hale para estudiar la relación entre el acotamiento y la periodicidad de soluciones para algunas EDP no homogéneas lineales con retardo. Se entrega un ejemplo al final de este trabajo para mostrar la aplicabilidad de los resultados teóricos.

  • English

    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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