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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 490, Pages 9–12
DOI: https://doi.org/10.31857/S2686954320010117 (Mi danma23) 		 
This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Stieltjes differential in impulse nonlinear problems

A. D. Baev, D. A. Chechin, M. B. Zvereva, S. A. Shabrov

Voronezh State University, Voronezh, Russia
Full-text PDF (140 kB) Citations (3)
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DOI: https://doi.org/10.31857/S2686954320010117
Abstract: An impulse nonlinear problem admitting discontinuous solutions that are functions of bounded variation is studied. This problem models the deformation of a discontinuous string (chains of strings fastened together by springs) with elastic supports in the form of linear and nonlinear springs (for example, springs with different turns, whose deformations do not obey Hooke’s law). The model is described by a second-order differential equation with derivatives in special measures and Dirichlet boundary conditions. Existence theorems are proved, and conditions for the existence of nonnegative solutions are obtained.
Keywords: bounded variation function, Stieltjes integral, measure, derivative in measure Stieltjes string.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0037
Russian Science Foundation 19–11–00197
his work was supported by the Ministry of Education and Science of the Russian Federation (project no. 14.Z50.31.0037) and by the Russian Science Foundation (project no. 19-11-00197) and was performed at Voronezh State University (Theorems 1–4).
Presented: E. I. Moiseev
Received: 11.10.2019
Revised: 14.10.2019
Accepted: 05.11.2019
English version:
Doklady Mathematics, 2020, Volume 101, Issue 1, Pages 5–8
DOI: https://doi.org/10.1134/S1064562420010111
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
Citation: A. D. Baev, D. A. Chechin, M. B. Zvereva, S. A. Shabrov, “Stieltjes differential in impulse nonlinear problems”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020), 9–12; Dokl. Math., 101:1 (2020), 5–8
Citation in format AMSBIB
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\paper Stieltjes differential in impulse nonlinear problems
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\transl
\jour Dokl. Math.
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\pages 5--8
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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