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Mat. Zametki, 2009, Volume 85, Issue 3, Pages 408–420 (Mi mz4128)  

This article is cited in 6 scientific papers (total in 6 papers)

The Behavior of Solutions of Semilinear Elliptic Equations of Second Order of the Form $Lu=e^u$ in the Infinite Cylinder

A. V. Neklyudov

N. E. Bauman Moscow State Technical University

Abstract: We consider a semilinear elliptic equation of second order with variable coefficients of the form $Lu=e^u$ in the semi-infinite cylinder whose solution satisfies a homogeneous Neumann condition on the lateral surface of the cylinder.

Keywords: semilinear elliptic equation, Neumann boundary condition, Dirichlet integral, Poincaré inequality, Hölder's inequality

DOI: https://doi.org/10.4213/mzm4128

Full text: PDF file (479 kB)
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English version:
Mathematical Notes, 2009, 85:3, 397–408

Bibliographic databases:

UDC: 517.956.223
Received: 10.10.2007

Citation: A. V. Neklyudov, “The Behavior of Solutions of Semilinear Elliptic Equations of Second Order of the Form $Lu=e^u$ in the Infinite Cylinder”, Mat. Zametki, 85:3 (2009), 408–420; Math. Notes, 85:3 (2009), 397–408

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Neklyudov, “The Behavior of Solutions of the Nonlinear Biharmonic Equation in an Unbounded Domain”, Math. Notes, 95:2 (2014), 226–233  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. A. V. Neklyudov, “On the absence of global solutions of the Gauss equation and solutions in external areas”, Russian Math. (Iz. VUZ), 58:1 (2014), 47–51  mathnet  crossref
    3. A. V. Neklyudov, “Behavior of solutions to Gauss–Bieberbach–Rademacher equation on plane”, Ufa Math. J., 6:3 (2014), 85–94  mathnet  crossref  elib
    4. A. V. Nekludov, “On solutions of second order elliptic equations in cylindrical domains”, Ufa Math. J., 8:4 (2016), 131–143  mathnet  crossref  isi  elib
    5. A. V. Neklyudov, “Asimptotika reshenii dvumernogo uravneniya Gaussa—Biberbakha—Rademakhera s peremennymi koeffitsientami vo vneshnei oblasti”, Sib. elektron. matem. izv., 15 (2018), 338–354  mathnet  crossref
    6. A. V. Neklyudov, “On the Robin Problem for Second-Order Elliptic Equations in Cylindrical Domains”, Math. Notes, 103:3 (2018), 430–446  mathnet  crossref  crossref  isi  elib
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