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Matematicheskie Zametki, 1998, Volume 63, Issue 1, Pages 95–105
DOI: https://doi.org/10.4213/mzm1251
(Mi mzm1251)
 

This article is cited in 31 scientific papers (total in 31 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
References:
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.
Received: 27.06.1996
English version:
Mathematical Notes, 1998, Volume 63, Issue 1, Pages 84–93
DOI: https://doi.org/10.1007/BF02316146
Bibliographic databases:
UDC: 517
Language: Russian
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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\paper On Grushin's equation
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\yr 1998
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\issue 1
\pages 95--105
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\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 1
\pages 84--93
\crossref{https://doi.org/10.1007/BF02316146}
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Linking options:
  • https://www.mathnet.ru/eng/mzm1251
  • https://doi.org/10.4213/mzm1251
  • https://www.mathnet.ru/eng/mzm/v63/i1/p95
  • This publication is cited in the following 31 articles:
    1. N. Q. Nga, N. M. Tri, D. A. Tuan, “Pólya–Szegö type inequality and imbedding theorems for weighted Sobolev spaces”, Anal.Math.Phys., 14:2 (2024)  crossref
    2. D. T. Luyen, N. M. Tri, D. A. Tuan, “Nontrivial solutions of the Dirichlet problems for semilinear degenerate elliptic equations”, Math. Notes, 116:5 (2024), 1051–1063  mathnet  mathnet  crossref
    3. Luyen D.T. Cuong Ph.V., “Multiple Solutions to Boundary Value Problems For Semilinear Strongly Degenerate Elliptic Differential Equations”, Rend. Circ. Mat. Palermo, 71:1 (2022), 495–513  crossref  isi
    4. Duong Trong Luyen, Ha Tien Ngoan, Phung Thi Kim Yen, “Existence and Non-Existence of Solutions For Semilinear Bi-Delta(Gamma)-Laplace Equation”, Bull. Malays. Math. Sci. Soc., 45:2 (2022), 819–838  crossref  isi
    5. Alfalqi S., “Non-Existence Results For Stable Solutions to Weighted Elliptic Systems Including Advection Terms”, Mathematics, 10:2 (2022), 252  crossref  isi
    6. Duong Trong Luyen, Le Thi Hong Hanh, “Infinitely many solutions for perturbed Λγ-Laplace equations”, Georgian Mathematical Journal, 29:6 (2022), 863  crossref
    7. Duong Trong Luyen, Le Thi Hong Hanh, “Three nontrivial solutions of boundary value problems for semilinear $\Delta_{\gamma}-$Laplace equation”, bspm, 40 (2022), 1  crossref
    8. Xiaohuan Wang, Jihui Zhang, “Optimal Regularity of a Degenerate Elliptic Equation”, J Nonlinear Math Phys, 30:1 (2022), 254  crossref
    9. Duong Trong Luyen, “Infinitely Many Solutions For Semilinear Strongly Degenerate Elliptic Differential Equations With Lack of Symmetry”, Acta Appl. Math., 175:1 (2021), 3  crossref  isi
    10. Duong Trong Luyen, Ninh Tien Nam, “Infinitely Many Solutions For Fourth-Order Semilinear Delta(Gamma) - Laplace Equation in R-N”, J. Elliptic Parabol. Equat., 7:2 (2021), 977–988  crossref  isi
    11. Lamberti P.D., Luzzini P., Musolino P., “Shape Perturbation of Grushin Eigenvalues”, J. Geom. Anal., 31:11 (2021), 10679–10717  crossref  isi
    12. Hamdani M.K., “Multiple Solutions For Grushin Operator Without Odd Nonlinearity”, Asian-Eur. J. Math., 13:7 (2020), 2050131  crossref  isi
    13. Luyen D.T. Tri N.M., “Infinitely Many Solutions For a Class of Perturbed Degenerate Elliptic Equations Involving the Grushin Operator”, Complex Var. Elliptic Equ., 65:12 (2020), 2135–2150  crossref  isi
    14. Duong Trong Luyen, “Existence of Nontrivial Solution For Fourth-Order Semilinear Delta(Gamma)-Laplace Equation R-N”, Electron. J. Qual. Theory Differ., 2019, no. 78, 1–12  crossref  isi
    15. Loiudice A., “Asymptotic Estimates and Nonexistence Results For Critical Problems With Hardy Term Involving Grushin-Type Operators”, Ann. Mat. Pura Appl., 198:6 (2019), 1909–1930  crossref  isi
    16. 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
    17. Rahal B. Hamdani M.K., “Infinitely Many Solutions For Delta(Alpha)-Laplaceequations With Sign-Changing Potential”, J. Fixed Point Theory Appl., 20:4 (2018), UNSP 137  crossref  mathscinet  isi  scopus
    18. Kogoj A.E. Lanconelli E., “Linear and Semilinear Problems Involving Delta(Lambda)-Laplacians”, Electron. J. Differ. Equ., 2018, no. 25, 167–178  mathscinet  zmath  isi
    19. D. T. Luyen, “Two Nontrivial Solutions of Boundary-Value Problems for Semilinear $\Delta_{\gamma}$-Differential Equations”, Math. Notes, 101:5 (2017), 815–823  mathnet  mathnet  crossref  isi  scopus
    20. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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