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Matematicheskie Zametki, 2015, Volume 97, Issue 3, Pages 440–447
DOI: https://doi.org/10.4213/mzm10601 (Mi mzm10601) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Estimates of the Volume of Solutions of Differential Equations with Hukuhara Derivative

E. V. Ocheretnyuka, V. I. Slyn'kob

a Cherkasy State Technological University
b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine
Full-text PDF (443 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm10601
Abstract: For a class of nonlinear differential equations with Hukuhara derivative, lower bounds for the volume of their solutions are obtained. A. D. Aleksandrov's classical inequalities for mixed volumes combined with the comparison method are used.
Keywords: nonlinear differential equation, Hukuhara derivative, volume of solutions of a differential equation, Aleksandrov's inequalities for mixed volumes, Lyapunov function, Hausdorff metric, Steiner's formula, Aumann integral.
Funding agency Grant number
Verkhovna Rada of Ukraine
This work was supported by the Stipend of the Supreme Rada of Ukraine.
Received: 12.01.2014
Revised: 22.04.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 3, Pages 431–437
DOI: https://doi.org/10.1134/S0001434615030141
Bibliographic databases:
Document Type: Article
UDC: 517.929.21
Language: Russian
Citation: E. V. Ocheretnyuk, V. I. Slyn'ko, “Estimates of the Volume of Solutions of Differential Equations with Hukuhara Derivative”, Mat. Zametki, 97:3 (2015), 440–447; Math. Notes, 97:3 (2015), 431–437
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm10601
  • https://doi.org/10.4213/mzm10601
  • https://www.mathnet.ru/eng/mzm/v97/i3/p440
    • This publication is cited in the following 3 articles:
    1. V. S. Denysenko, “On technical stability for sets of trajectories of discrete systems”, Russian Math. (Iz. VUZ), 64:7 (2020), 54–65  mathnet  crossref  crossref  isi
    2. V. I. Slyn'ko, “Solution Area for a Class of Linear Differential Equations with Hukuhara Derivative”, Math. Notes, 105:2 (2019), 285–290  mathnet  crossref  crossref  mathscinet  isi  elib
    3. I. V. Atamas, V. I. Slyn'ko, “Liouville formula for some classes of differential equations with the hukuhara derivative”, Differ. Equ., 55:11 (2019), 1407–1419  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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