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Shadowing for nonautonomous and nonlinear dynamics with impulses

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Abstract

For a large class of nonautonomous semilinear impulsive differential equations, we formulate sufficient conditions under which in a vicinity of each approximate solution, we can construct an exact solution. An important feature of our result is that it is applicable to situations when the linear part is not hyperbolic. In addition, we establish analogous result in the case of discrete time.

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Acknowledgements

L.B. was partially supported by a CNPq-Brazil PQ fellowship under Grant No. 306484/2018-8. D.D. was supported in part by Croatian Science Foundation under the project IP-2019-04-1239 and by the University of Rijeka under the projects uniri-prirod-18-9 and uniri-pr-prirod-19-16. L.S. was fully supported by Croatian Science Foundation under the project IP-2019-04-1239.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, CEP 91509-900, Porto Alegre, RS, Brazil

    Lucas Backes

  2. Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000, Rijeka, Croatia

    Davor Dragičević & Lokesh Singh

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  1. Lucas Backes
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  2. Davor Dragičević
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  3. Lokesh Singh
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Correspondence to Lucas Backes.

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Communicated by Adrian Constantin.

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Backes, L., Dragičević, D. & Singh, L. Shadowing for nonautonomous and nonlinear dynamics with impulses. Monatsh Math 198, 485–502 (2022). https://doi.org/10.1007/s00605-021-01629-2

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