Existence of ω-periodic solutions for a delayed chemostat with periodic inputs. (October 2020)

• Record Type: Journal Article
• Authors: Amster, Pablo; Robledo, Gonzalo; Sepúlveda, Daniel
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Chemostat -- Periodic solutions -- Delay differential equations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103134
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper proposes an ω -periodic version of the Ellermeyer model of delayed chemostat. We obtain a sufficient condition ensuring the existence of a positive ω -periodic solution. Our proof is based on the application of the generalized continuation theorem. In addition, as a consequence of the implicit function theorem, we obtain a uniqueness result for sufficiently small delays.