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A Filippov-Type Lemma for Stieltjes Differential Inclusions with Supremum

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  • Bianca Satco

    (Faculty of Electrical Engineering and Computer Science, “Stefan cel Mare” University of Suceava, Universitatii 13, 720229 Suceava, Romania)

Abstract

The aim of this paper is to generalize the classical Filippov lemma to the framework of Cauchy differential set-valued problems involving the supremum of the unknown function on a past interval and its Stieltjes derivative with respect to a left-continuous non-decreasing function. To highlight the wide spectrum of the result (coming from the fact that this setting covers the theories of ordinary differential or difference problems, impulsive problems or problems on time scales), as a consequence, a Filippov-type lemma for dynamic inclusions on time scales with supremum is obtained.

Suggested Citation

  • Bianca Satco, 2024. "A Filippov-Type Lemma for Stieltjes Differential Inclusions with Supremum," Mathematics, MDPI, vol. 12(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3605-:d:1523643
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    References listed on IDEAS

    as
    1. Andrzej Fryszkowski & Jacek Sadowski, 2021. "Filippov lemma for measure differential inclusion," Mathematische Nachrichten, Wiley Blackwell, vol. 294(3), pages 580-602, March.
    2. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
    3. S. G. Hristova & A. Georgieva, 2011. "Practical Stability in terms of Two Measures for Impulsive Differential Equations with “Supremumâ€," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-13, October.
    Full references (including those not matched with items on IDEAS)

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