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Lipschitz Stability in Terms of Two Measures for Kurzweil Equations and Applications

Author

Listed:
  • Yingying Wang

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

  • Zhinan Xia

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

Abstract

For generalized ordinary differential equations, sufficient criteria are given for the Lipschitz stability in terms of two measures of the trivial solutions. As an application, we apply our main results by studying the Lipschitz stability for measure differential equations and impulsive differential equations. Compared to the classical ones, the conditions here regarding the functions are more general.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2006-:d:1131016
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    References listed on IDEAS

    as
    1. 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.
    2. Márcia Federson & Jaqueline G. Mesquita & Eduard Toon, 2015. "Lyapunov theorems for measure functional differential equations via Kurzweil-equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(13), pages 1487-1511, September.
    3. Taher S. Hassan & Qingkai Kong & Bassant M. El-Matary, 2023. "Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
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