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Mat. Zametki, 1998, Volume 63, Issue 1, Pages 95–105 (Mi mz1251)  

This article is cited in 11 scientific papers (total in 11 papers)

On Grushin's equation

Nguyen Minh Triab

a Institute of Mathematics, National Centre for Natural Science and Technology
b International Centre for Theoretical Physics

Abstract: The paper deals with nonlinear problems for equations of Grushin type. We prove some nonexistence results via Pokhozhaev's identity. In the rest of the paper we prove some results on smoothness near the boundary of eigenfunctions by using an explicit formula for fundamental solutions and the Kelvin transform for the operator.

DOI: https://doi.org/10.4213/mzm1251

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English version:
Mathematical Notes, 1998, 63:1, 84–93

Bibliographic databases:

UDC: 517
Received: 27.06.1996

Citation: Nguyen Minh Tri, “On Grushin's equation”, Mat. Zametki, 63:1 (1998), 95–105; Math. Notes, 63:1 (1998), 84–93

Citation in format AMSBIB
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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. Bieske, T, “Viscosity solutions on Grushin-type planes”, Illinois Journal of Mathematics, 46:3 (2002), 893  mathscinet  zmath  isi
    2. Lupo, D, “Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types”, Communications on Pure and Applied Mathematics, 56:3 (2003), 403  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Ke T., “Existence of Non-Negative Solutions for a Semilinear Degenerate Elliptic System”, Proceedings of the International Conference on Abstract and Applied Analysis, eds. Chuong N., Nirenberg L., Tutschke W., World Scientific Publ Co Pte Ltd, 2004, 203–212  mathscinet  isi
    4. Bieske, T, “The P-Laplace equation on a class of Grushin-type spaces”, Proceedings of the American Mathematical Society, 134:12 (2006), 3585  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Lupo D., Payne K., Popivanov N., “Nonexistence of Nontrivial Solutions for Supercritical Equations of Mixed Elliptic-Hyperbolic Type”, Contributions to Nonlinear Analysis: a Tribute to D. G. de Figueiredo on the Occasion of His 70th Birthday, Progress in Nonlinear Differential Equations and their Applications, 66, eds. Costa D., Lopes O., Manasevich R., Rabinowitz P., Ruf B., Tomei C., Birkhauser Verlag Ag, 2006, 371–390  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Monticelli D.D., “Maximum Principles and the Method of Moving Planes for a Class of Degenerate Elliptic Linear Operators”, J. Eur. Math. Soc., 12:3 (2010), 611–654  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Mihailescu M., Morosanu G., Stancu-Dumitru D., “Equations Involving a Variable Exponent Grushin-Type Operator”, Nonlinearity, 24:10 (2011), 2663–2680  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Thuy P.T., Tri N.M., “Nontrivial Solutions to Boundary Value Problems for Semilinear Strongly Degenerate Elliptic Differential Equations”, NoDea-Nonlinear Differ. Equ. Appl., 19:3 (2012), 279–298  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Luyen D.T., Tri N.M., “On Boundary Value Problem for Semilinear Degenerate Elliptic Differential Equations”, 5th International Conference on Research and Education in Mathematics (Icrem5), AIP Conference Proceedings, 1450, eds. Baskoro E., Suprijanto D., Amer Inst Physics, 2012, 13–17  crossref  adsnasa  isi  scopus  scopus
    10. Mihailescu M., Stancu-Dumitru D., Varga C., “on the Spectrum of a Baouendi-Grushin Type Operator: An Orlicz-Sobolev Space Setting Approach”, NoDea-Nonlinear Differ. Equ. Appl., 22:5 (2015), 1067–1087  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Duong Trong Luyen Nguyen Mirth Tri, “Existence of Infinitely Many Solutions For Semilinear Degenerate Schrodinger Equations”, J. Math. Anal. Appl., 461:2 (2018), 1271–1286  crossref  mathscinet  zmath  isi  scopus  scopus
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