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Mat. Zametki, 2015, Volume 97, Issue 5, Pages 733–748 (Mi mz10654)  

This article is cited in 5 scientific papers (total in 5 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

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).


DOI: https://doi.org/10.4213/mzm10654

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English version:
Mathematical Notes, 2015, 97:5, 745–758

Bibliographic databases:

Document Type: Article
UDC: 517
Received: 09.10.2014

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. L. Tasevich, “Smoothness of generalized solutions of the Dirichlet problem for strongly elliptic functional differential equations with orthotropic contractions”, Journal of Mathematical Sciences, 233:4 (2018), 541–554  mathnet  crossref
    2. A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. L. Tasevich, “Analysis of functional-differential equation with orthotropic contractions”, Math. Model. Nat. Phenom., 12:6, SI (2017), 240–248  crossref  zmath  isi  scopus
    4. L. E. Rossovskii, A. L. Tasevich, “Unique solvability of a functional-differential equation with orthotropic contractions in weighted spaces”, Differ. Equ., 53:12 (2017), 1631–1644  crossref  mathscinet  zmath  isi  scopus
    5. A. L. Skubachevskii, “Ob odnom klasse funktsionalno-differentsialnykh operatorov, udovletvoryayuschikh gipoteze Kato”, Algebra i analiz, 30:2 (2018), 249–273  mathnet  elib
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