V. P. Burskii, E. A. Buryachenko, “Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk”, Mat. Zametki, 77:4 (2005), 498–508; Math. Notes, 77:4 (2005), 461

Matematicheskie Zametki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Matematicheskie Zametki, 2005, Volume 77, Issue 4, Pages 498–508
DOI: https://doi.org/10.4213/mzm2508 (Mi mzm2508)

This article is cited in 14 scientific papers (total in 14 papers)

Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk

V. P. Burskii, E. A. Buryachenko

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Full-text PDF (226 kB) Citations (14)

References:

PDF

HTML

DOI: https://doi.org/10.4213/mzm2508

Abstract: In this paper, we obtain a necessary and sufficient condition for the nontrivial solvability of homogeneous Dirichlet problems in the disk for linear equations of arbitrary even order $2m$ with constant complex coefficients and homogeneous nondegenerate symbol in general position. The cases $m=1,2,3$ are studied separately. For the case $m=2$, we consider examples of real elliptic systems reducible to single equations with constant complex coefficients for which the homogeneous Dirichlet problem in the disk has a countable set of linearly independent polynomial solutions.

Received: 10.01.2000
Revised: 09.02.2004

English version:
Mathematical Notes, 2005, Volume 77, Issue 4, Pages 461–470
DOI: https://doi.org/10.1007/s11006-005-0044-9

Bibliographic databases:

UDC: 517.946

Language: Russian

Citation: V. P. Burskii, E. A. Buryachenko, “Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk”, Mat. Zametki, 77:4 (2005), 498–508; Math. Notes, 77:4 (2005), 461–470

Citation in format AMSBIB

\Bibitem{BurBur05}

\by V.~P.~Burskii, E.~A.~Buryachenko

\paper Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk

\jour Mat. Zametki

\yr 2005

\vol 77

\issue 4

\pages 498--508

\mathnet{http://mi.mathnet.ru/mzm2508}

\crossref{https://doi.org/10.4213/mzm2508}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2178013}

\zmath{https://zbmath.org/?q=an:1112.35043}

\elib{https://elibrary.ru/item.asp?id=9155800}

\transl

\jour Math. Notes

\yr 2005

\vol 77

\issue 4

\pages 461--470

\crossref{https://doi.org/10.1007/s11006-005-0044-9}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000228965300015}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-20244373176}

Linking options:

https://www.mathnet.ru/eng/mzm2508

https://doi.org/10.4213/mzm2508

https://www.mathnet.ru/eng/mzm/v77/i4/p498

This publication is cited in the following 14 articles:

Yuliia Andreieva, Kateryna Buryachenko, “Qualitative analysis of fourth-order hyperbolic equations”, Front. Appl. Math. Stat., 10 (2024)
A. H. Babayan, “On a Dirichlet Problem for Properly Elliptic Equation in the Space of Continuous Functions”, Lobachevskii J Math, 45:12 (2024), 6011
Kateryna Buryachenko, “Maximum principle for the weak solutions of the Cauchy problem for the fourth‐order hyperbolic equations”, Proc Appl Math and Mech, 2023
Ya. O. Baranetskij, P. I. Kalenyuk, “Nonlocal Problem with Multipoint Perturbations of Dirichlet Conditions for Even-Order Partial Differential Equations with Constant Coefficients”, J Math Sci, 256:4 (2021), 375
V. P. Burskii, E. V. Lesina, “On boundary value problems for an improperly elliptic equation in a circle”, Comput. Math. Math. Phys., 60:8 (2020), 1306–1321
Ya. O. Baranetskij, P. І. Kalenyuk, M. І. Kopach, “Nonlocal Multipoint Problem for Partial Differential Equations of Even Order with Constant Coefficients”, J Math Sci, 249:3 (2020), 307
Babayan A.H., “On a Dirichlet Problem For One Improperly Elliptic Equation”, Complex Var. Elliptic Equ., 64:5 (2019), 825–837
V. P. Burskii, “Equation–Domain Duality in the Dirichlet Problem for General Differential Equations in the Space $L_2$”, Proc. Steklov Inst. Math., 306 (2019), 33–42
Armenak H. Babayan, Seyran H. Abelyan, Springer Proceedings in Mathematics & Statistics, 291, Modern Methods in Operator Theory and Harmonic Analysis, 2019, 317
A. O. Babayan, S. O. Abelyan, “Defect Numbers of the Dirichlet Problem for a Properly Elliptic Sixth-Order Equation”, Math. Notes, 104:3 (2018), 339–347
Baranetskij Ya.O. Ivasiuk I.Ya. Kalenyuk I P. Solomko V A., “The Nonlocal Boundary Problem With Perturbations of Antiperiodicity Conditions For the Eliptic Equation With Constant Coefficients”, Carpathian Math. Publ., 10:2 (2018), 215–234
V. S. Il'kiv, “Nonuniqueness conditions for the solutions of the Dirichlet problem in a unit disk in terms of the coefficients of differential equation”, J Math Sci, 194:2 (2013), 182
Buryachenko E.A., “Conditions of nontrivial solvability of the homogeneous Dirichlet problem for equations of any even order in the case of multiple characteristics without slope angles”, Ukrainian Math. J., 62:5 (2010), 676–690
Render H., “Cauchy, Goursat and Dirichlet Problems for Holomorphic Partial Differential Equations”, Comput. Methods Funct. Theory, 10:2 (2010), 519–554

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

Statistics & downloads:
Abstract page:	597
Full-text PDF :	252
References:	87
First page:	1

Что такое QR-код?

Registration to the website

Logotypes