Asymptotic stability of solutions for some classes of impulsive differential equations with distributed delay

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 sta...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 61; p. 103324
Main Author Rubbioni, Paola
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.10.2021
Subjects
Asymptotic stability
Functional delay
Gronwall–Bellmann inequality
Impulsive problems
Population dynamics
Semilinear differential equations
Impulsive problems
Asymptotic stability
Semilinear differential equations
Population dynamics
Functional delay
Gronwall–Bellmann inequality
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Summary: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.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2021.103324