Loading [MathJax]/jax/output/SVG/config.js
Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
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, 2021, Volume 110, Issue 2, Pages 239–257
DOI: https://doi.org/10.4213/mzm12596 (Mi mzm12596) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University
b Saint Petersburg State University
Full-text PDF (561 kB) Citations (3)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm12596
Abstract: For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for almost all values of the spatial variable. Such solutions are said to be semiregular. An upper-and-lower-solution principle is established for the existence of semiregular solutions to elliptic systems with discontinuous nonlinearities. This principle is used to prove theorems on the existence of semiregular solutions of elliptic systems with discontinuous nonlinearities, in particular, nontrivial solutions of problems with a parameter. Examples of classes of nonlinearities with separated variables satisfying the conditions of our theorems are given.
Keywords: elliptic system, discontinuous nonlinearity, semiregular solution, upper solution, lower solution.
Received: 15.10.2019
Revised: 19.03.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 2, Pages 226–241
DOI: https://doi.org/10.1134/S0001434621070245
Bibliographic databases:
Document Type: Article
UDC: 517.956.2
Language: Russian
Citation: V. N. Pavlenko, D. K. Potapov, “Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities”, Mat. Zametki, 110:2 (2021), 239–257; Math. Notes, 110:2 (2021), 226–241
Citation in format AMSBIB
\Bibitem{PavPot21}
\by V.~N.~Pavlenko, D.~K.~Potapov
\paper Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities
\jour Mat. Zametki
\yr 2021
\vol 110
\issue 2
\pages 239--257
\mathnet{http://mi.mathnet.ru/mzm12596}
\crossref{https://doi.org/10.4213/mzm12596}
\elib{https://elibrary.ru/item.asp?id=47028151}
\transl
\jour Math. Notes
\yr 2021
\vol 110
\issue 2
\pages 226--241
\crossref{https://doi.org/10.1134/S0001434621070245}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000687705200024}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85113802035}
Linking options:
  • https://www.mathnet.ru/eng/mzm12596
  • https://doi.org/10.4213/mzm12596
  • https://www.mathnet.ru/eng/mzm/v110/i2/p239
    • This publication is cited in the following 3 articles:
    1. N. Nefedov, B. Tishchenko, N. Levashova, “An algorithm for construction of the asymptotic approximation of a stable stationary solution to a diffusion equation system with a discontinuous source function”, Algorithms, 16:8 (2023), 359  crossref
    2. V. N. Pavlenko, D. K. Potapov, “Semiregular solutions of elliptic boundary-value problems with discontinuous nonlinearities of exponential growth”, Sb. Math., 213:7 (2022), 1004–1019  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. V. N. Pavlenko, D. K. Potapov, “One class of quasilinear elliptic type equations with discontinuous nonlinearities”, Izv. Math., 86:6 (2022), 1162–1178  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:259
    Full-text PDF :81
    References:48
    First page:8
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025