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Stability Analysis of Second Order Impulsive Differential Equations

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Abstract

In this paper, we apply the strongly continuous cosine family of bounded linear operators to study the explicit representation of solutions for second order linear impulsive differential equations, and we give sufficient conditions for asymptotical stability of solutions. In addition we study the exponential stability of the linear perturbed problem. Existence and uniqueness of solutions of the initial value problem for nonlinear second order impulsive differential equations is obtained and we present Ulam–Hyers–Rassias stability results. Examples are provided to illustrate the applicability of our results.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Qian Wen & JinRong Wang

  2. School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland

    Donal O’Regan

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  1. Qian Wen
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  2. JinRong Wang
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  3. Donal O’Regan
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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016)

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Wen, Q., Wang, J. & O’Regan, D. Stability Analysis of Second Order Impulsive Differential Equations. Qual. Theory Dyn. Syst. 21, 54 (2022). https://doi.org/10.1007/s12346-022-00587-w

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  • DOI: https://doi.org/10.1007/s12346-022-00587-w

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