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Mathematics of the USSR-Sbornik, 1970, Volume 11, Issue 2, Pages 171–188
DOI: https://doi.org/10.1070/SM1970v011n02ABEH001133
(Mi sm3443)
 

This article is cited in 37 scientific papers (total in 38 papers)

On the eigenfunctions of quasilinear elliptic problems

S. I. Pokhozhaev
References:
Abstract: The existence or nonexistence of eigenfunctions is examined for quasilinear elliptic equations of arbitrary even order with homogeneous Dirichlet boundary conditions.
Bibliography: 12 titles.
Received: 27.05.1969
Bibliographic databases:
Document Type: Article
UDC: 517.945.9
Language: English
Original paper language: Russian
Citation: S. I. Pokhozhaev, “On the eigenfunctions of quasilinear elliptic problems”, Math. USSR-Sb., 11:2 (1970), 171–188
Citation in format AMSBIB
\Bibitem{Pok70}
\by S.~I.~Pokhozhaev
\paper On~the eigenfunctions of quasilinear elliptic problems
\jour Math. USSR-Sb.
\yr 1970
\vol 11
\issue 2
\pages 171--188
\mathnet{http://mi.mathnet.ru/eng/sm3443}
\crossref{https://doi.org/10.1070/SM1970v011n02ABEH001133}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=273200}
\zmath{https://zbmath.org/?q=an:0217.13203}
Linking options:
  • https://www.mathnet.ru/eng/sm3443
  • https://doi.org/10.1070/SM1970v011n02ABEH001133
  • https://www.mathnet.ru/eng/sm/v124/i2/p192
  • This publication is cited in the following 38 articles:
    1. Bingyu Kou, Tianqing An, Zeyan Wang, “The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)”, Bound Value Probl, 2020:1 (2020)  crossref
    2. Ze Cheng, Congming Li, “Shooting method with sign-changing nonlinearity”, Nonlinear Analysis: Theory, Methods & Applications, 114 (2015), 2  crossref  mathscinet  zmath
    3. Pokhozhaev S.I., “Critical Nonlinearities in Partial Differential Equations”, Russ. J. Math. Phys., 20:4 (2013), 476–491  crossref  mathscinet  zmath  isi
    4. Xiaotao Huang, Yi Cao, “Critical exponents and Pohozhaev identities of some partial differential equations”, Mathematical and Computer Modelling, 2012  crossref  mathscinet
    5. Kostomarov D.P., Sheina E.A., “Zadacha o kratnykh sobstvennykh znacheniyakh i polozhitelnykh sobstvennykh funktsiyakh dlya odnomernogo kvazilineinogo uravneniya vtorogo poryadka”, Differentsialnye uravneniya, 48:8 (2012), 1096–1096  zmath  elib
    6. M. O. Korpusov, “On the uniqueness of the solution of a nonlinear eigenmode problem”, Comput. Math. Math. Phys., 51:4 (2011), 597–601  mathnet  crossref  mathscinet  isi  elib
    7. Yuri Bozhkov, Peter J. Olver, “Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics”, SIGMA, 7 (2011), 055, 9 pp.  mathnet  crossref  mathscinet
    8. M. O. Korpusov, A. G. Sveshnikov, “On a nonlinear eigenmode problem in semiconductor theory”, Comput. Math. Math. Phys., 51:5 (2011), 816–823  mathnet  crossref  mathscinet  isi  elib
    9. V. A. GALAKTIONOV, S. R. SVIRSHCHEVSKII, “INVARIANT SOLUTIONS OF NONLINEAR DIFFUSION EQUATIONS WITH MAXIMAL SYMMETRY ALGEBRA”, J. Nonlinear Math. Phys, 18:supp01 (2011), 107  crossref  mathscinet  zmath
    10. Kostomarov D.P., Sheina E.A., “Kratnye sobstvennye znacheniya odnomernoi kvazilineinoi zadachi”, Doklady akademii nauk, 438:2 (2011), 172–175  zmath  elib
    11. Kostomarov D.P., “Odnomernaya kvazilineinaya zadacha na sobstvennye znacheniya i sobstvennye funktsii”, Differentsialnye uravneniya, 47:6 (2011), 785–795  mathscinet  zmath  elib
    12. Elvise Berchio, Filippo Gazzola, “Positive solutions to a linearly perturbed critical growth biharmonic problem”, DCDS-S, 4:4 (2010), 809  crossref  mathscinet
    13. Yavdat Il’yasov, Youri Egorov, “Hopf boundary maximum principle violation for semilinear elliptic equations”, Nonlinear Analysis: Theory, Methods & Applications, 72:7-8 (2010), 3346  crossref  mathscinet  zmath
    14. Pohozaev, SI, “Critical Nonlinearities in Partial Differential Equations”, Milan Journal of Mathematics, 77:1 (2009), 127  crossref  mathscinet  zmath  isi  elib
    15. M. Lazzo, P.G. Schmidt, “Oscillatory radial solutions for subcritical biharmonic equations”, Journal of Differential Equations, 247:5 (2009), 1479  crossref  mathscinet  zmath
    16. Yuri Bozhkov, Enzo Mitidieri, “Lie Symmetries and Criticality of Semilinear Differential Systems”, SIGMA, 3 (2007), 053, 17 pp.  mathnet  crossref  mathscinet  zmath
    17. M. O. Korpusov, A. G. Sveshnikov, ““Destruction” of the solution of a strongly nonlinear equation of pseudoparabolic type with double nonlinearity”, Math. Notes, 79:6 (2006), 820–840  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. Ilaria Fragalà, Filippo Gazzola, Bernd Kawohl, “Existence and nonexistence results for anisotropic quasilinear elliptic equations”, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 21:5 (2004), 715  crossref  mathscinet  zmath
    19. Victor A. Galaktionov, John R. King, “Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents”, Journal of Differential Equations, 189:1 (2003), 199  crossref  mathscinet  zmath
    20. Marie-Francoise Bidaut-Véron, Stanislav Pohozaev, “Nonexistence results and estimates for some nonlinear elliptic problems”, J Anal Math, 84:1 (2001), 1  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:1109
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    References:107
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