Asymptotic stability of solutions for some classes of impulsive differential equations with distributed delay. (October 2021)

• Record Type: Journal Article
• Authors: Rubbioni, Paola
• Is Part Of: Nonlinear analysis. Volume 61(2021)
• Publication Date: 2021-10
• Subjects: Asymptotic stability -- Impulsive problems -- Functional delay -- Population dynamics -- Gronwall–Bellmann inequality -- Semilinear differential equations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103324
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we show the asymptotic stability of the solutions of some differential equations with delay and subject to impulses. After proving the existence of mild solutions on the half-line, we give a Gronwall–Bellman-type theorem. These results are prodromes of the theorem on the asymptotic stability of the mild solutions to a semilinear differential equation with functional delay and impulses in Banach spaces and of its application to a parametric differential equation driving a population dynamics model.