Existence of periodic or nonnegative periodic solutions for totally nonlinear neutral differential equations with infinite delay

• Guerfi, Abderrahim ^[1] ; Ardjouni, Abdelouaheb ^[2]
  1. [1] University of Annaba.
  2. [2] University of Souk Ahras.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 6, 2022, págs. 1297-1319
• Idioma: inglés
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• Resumen

  • In this work, we investigate the existence of periodic or nonnegative periodic solutions for a totally nonlinear neutral differential equation with infinite delay. In the process, we convert the given neutral differential equation into an equivalent integral equation. Then, we employ Krasnoselskiǐ-Burton’s fixed point theorem to prove the existence of periodic or nonnegative periodic solutions. Two examples are provided to illustrate the obtained results.