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Matematicheskie Zametki, 2015, Volume 97, Issue 5, Pages 733–748
DOI: https://doi.org/10.4213/mzm10654 (Mi mzm10654) 		 
This article is cited in 16 scientific papers (total in 16 papers)

The First Boundary-Value Problem for Strongly Elliptic Functional-Differential Equations with Orthotropic Contractions

L. E. Rossovskii, A. L. Tasevich

Peoples Friendship University of Russia, Moscow
Full-text PDF (524 kB) Citations (16)
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DOI: https://doi.org/10.4213/mzm10654
Abstract: We obtain a number of necessary and sufficient strong ellipticity conditions for a functional-differential equation containing, in its leading part, orthotropic contractions of the argument of the unknown function. We establish the unique solvability of the first boundary-value problem and the discreteness, semiboundedness, and sectorial structure of its spectrum.
Keywords: strong elliptic functional-differential equation, first boundary-value problem, orthotropic contraction, Gårding-type inequality, strong ellipticity condition, Plancherel's theorem, Fourier transform, Riesz theorem, difference operator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.1974.2014/К
This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 1.1974.2014/K).
Received: 09.10.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 5, Pages 745–758
DOI: https://doi.org/10.1134/S0001434615050090
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: L. E. Rossovskii, A. L. Tasevich, “The First Boundary-Value Problem for Strongly Elliptic Functional-Differential Equations with Orthotropic Contractions”, Mat. Zametki, 97:5 (2015), 733–748; Math. Notes, 97:5 (2015), 745–758
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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