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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 2, Pages 127–150 (Mi izv4088)  

This article is cited in 1 scientific paper (total in 1 paper)

The Bohl index of a homogeneous parabolic inclusion

V. S. Klimov

P. G. Demidov Yaroslavl State University

Abstract: The Bohl index is associated with a one-parameter family of multi-valued maps of elliptic type $\mathscr F(t)$, $0\le t<\infty$. It determines the asymptotic behaviour of solutions of the parabolic inclusion $0\in y'+\mathscr F(t)y$. Our main aim is to obtain lower bounds for the Bohl index. We study the nature of the dependence of solutions of the above inclusion on the initial value and the map $\mathscr F$. We prove that the Bohl index is stable with respect to perturbations that are small on the average.

Keywords: inclusion, homogeneity, stability, multi-valued map, solution.

DOI: https://doi.org/10.4213/im4088

Full text: PDF file (621 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:2, 347–370

Bibliographic databases:

UDC: 517.956
MSC: 34A60, 34C11, 34C29, 34D05, 35K20
Received: 16.02.2009
Revised: 13.04.2009

Citation: V. S. Klimov, “The Bohl index of a homogeneous parabolic inclusion”, Izv. RAN. Ser. Mat., 75:2 (2011), 127–150; Izv. Math., 75:2 (2011), 347–370

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  • https://doi.org/10.4213/im4088
  • http://mi.mathnet.ru/eng/izv/v75/i2/p127

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Klimov V.S., “Strength and Stability of the Bohl Index”, Differ. Equ., 51:5 (2015), 592–604  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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