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Algebra i Analiz, 2010, Volume 22, Issue 3, Pages 206–221 (Mi aa1193)  

This article is cited in 4 scientific papers (total in 4 papers)

Research Papers

Multiplicity of solutions of the Dirichlet problem for an equation with the $p$-Laplacian in a three-dimensional spherical layer

S. B. Kolonitskiĭ

St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

Abstract: The equation $-\Delta_pu=u^{q-1}$ with zero Dirichlet condition on the boundary is considered in a three-dimensional spherical layer. The existence of arbitrarily many distinct positive solutions in a sufficiently thin layer is proved.

Keywords: $p$-Laplacian, existence of many solutions.

Full text: PDF file (640 kB)
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English version:
St. Petersburg Mathematical Journal, 2011, 22:3, 485–495

Bibliographic databases:

Received: 22.09.2009

Citation: S. B. Kolonitskiǐ, “Multiplicity of solutions of the Dirichlet problem for an equation with the $p$-Laplacian in a three-dimensional spherical layer”, Algebra i Analiz, 22:3 (2010), 206–221; St. Petersburg Math. J., 22:3 (2011), 485–495

Citation in format AMSBIB
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\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 3
\pages 206--221
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\jour St. Petersburg Math. J.
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\vol 22
\issue 3
\pages 485--495
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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. S. B. Kolonitskii, “Multiplicity of 1D-concentrated positive solutions to the Dirichlet problem for an equation with $p$-Laplacian”, Funct. Anal. Appl., 49:2 (2015), 151–154  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. I. Nazarov, B. O. Neterebskii, “The multiplicity of positive solutions to the quasilinear equation generated by the Il'in–Caffarelli–Kohn–Nirenberg inequality”, J. Math. Sci. (N. Y.), 224:3 (2017), 448–455  mathnet  crossref  mathscinet
    3. Enin A., “Multiplicity of Positive Solutions For a Critical Quasilinear Neumann Problem”, Arch. Math., 109:3 (2017), 263–272  crossref  mathscinet  zmath  isi  scopus
    4. N. S. Ustinov, “Mnozhestvennost reshenii kraevykh zadach s drobnymi laplasianami Dirikhle i Nave”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 46, Zap. nauchn. sem. POMI, 459, POMI, SPb., 2017, 104–126  mathnet
  • Алгебра и анализ St. Petersburg Mathematical Journal
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