Measure (ω, c)-pseudo almost periodic functions and Lasota-Wazewska model with ergodic and unbounded oscillating oxygen demand

James Larrouy (1, 2) , Gaston N'Guérékata (3, 4)

1 Université des Antilles (Pôle Guadeloupe)
2 LAMIA - Laboratoire de Mathématiques Informatique et Applications [UR1_1]
3 Department of Mathematics, Morgan State University
4 Morgan State University

The primary aim of this work is to introduce a new class of functions called µ-(ω, c)-pseudo almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those µ-(ω, c)-pseudo almost periodic functions including two new composition results which play a crucial role for the existence of some µ-(ω, c)-pseudo almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the µ-(ω, c)pseudo almost periodic solutions for some models of Lasota-Wazewska equation with measure (ω, c)-pseudo almost periodic coefficient and mixed delays.

Mots clés: Composition Theorem; Lasota-Wazewska model; Unboundedness; c)-periodic; (ω; Periodic oscillations

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]; Algèbres d'opérateurs [math.OA]

James Larrouy, Gaston N'Guérékata. Measure (ω, c)-pseudo almost periodic functions and Lasota-Wazewska model with ergodic and unbounded oscillating oxygen demand. 2022. ⟨hal-03656239v1⟩