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Prolongation of solutions of measure differential equations and dynamic equations on time scales

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  • M. Federson
  • R. Grau
  • J. G. Mesquita

Abstract

In this paper, we prove the results on existence and uniqueness of the maximal solutions for measure differential equations, considering more general conditions on functions f and g by using the correspondence between the solutions of these equations and the solutions of generalized ODEs. Moreover, we prove these results for the dynamic equations on time scales, using the correspondence between the solutions of these last equations and the solutions of the measure differential equations.

Suggested Citation

  • M. Federson & R. Grau & J. G. Mesquita, 2019. "Prolongation of solutions of measure differential equations and dynamic equations on time scales," Mathematische Nachrichten, Wiley Blackwell, vol. 292(1), pages 22-55, January.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:1:p:22-55
    DOI: 10.1002/mana.201700420
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    Cited by:

    1. Andrade da Silva, F. & Bonotto, E.M. & Federson, M., 2024. "Stability for generalized stochastic equations," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    2. Pingkuo Liu & Jiahao Wu, 2023. "Game Analysis on Energy Enterprises’ Digital Transformation—Strategic Simulation for Guiding Role, Leading Role and Following Role," Sustainability, MDPI, vol. 15(13), pages 1-33, June.
    3. Yingying Wang & Zhinan Xia, 2023. "Lipschitz Stability in Terms of Two Measures for Kurzweil Equations and Applications," Mathematics, MDPI, vol. 11(9), pages 1-20, April.

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