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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| Published in | Nonlinear analysis: real world applications Vol. 61; p. 103324 |
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| Format | Journal Article |
| Language | English |
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01.10.2021
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 103324 |
| Author | Rubbioni, Paola |
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| Cites_doi | 10.5802/afst.723 10.1186/1687-1847-2012-34 10.1007/s00009-021-01730-8 10.1016/j.amc.2018.10.083 10.1016/j.na.2011.09.023 10.1016/j.jmaa.2016.04.024 10.1186/s13660-019-2250-0 10.1016/j.na.2011.06.055 10.1186/s13662-019-1994-7 10.1007/BF01203774 10.1007/s10957-014-0671-y 10.1088/0951-7715/29/3/823 10.1007/s00009-020-01574-8 |
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| Keywords | Impulsive problems Asymptotic stability Semilinear differential equations Population dynamics Functional delay Gronwall–Bellmann inequality |
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| SubjectTerms | Asymptotic stability Functional delay Gronwall–Bellmann inequality Impulsive problems Population dynamics Semilinear differential equations |
| Title | Asymptotic stability of solutions for some classes of impulsive differential equations with distributed delay |
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