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

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

This article is cited in 8 scientific papers (total in 8 papers)

Research Papers

Multiplicity of solutions of the Dirichlet problem for an equation with the

p

$p$ -Laplacian in a three-dimensional spherical layer

S. B. Kolonitskiĭ

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

Full-text PDF (640 kB) Citations (8)

References:

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Abstract: The equation

- Δ_{p} u = u^{q - 1}

$-\Delta_pu=u^{q-1}$ 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

$p$ -Laplacian, existence of many solutions.

Received: 22.09.2009

English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 3, Pages 485–495
DOI: https://doi.org/10.1090/S1061-0022-2011-01154-9

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: S. B. Kolonitskiǐ, “Multiplicity of solutions of the Dirichlet problem for an equation with the

p

$p$ -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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Linking options:

https://www.mathnet.ru/eng/aa1193

https://www.mathnet.ru/eng/aa/v22/i3/p206

This publication is cited in the following 8 articles:

D. E. Apushkinskaya, A. A. Arkhipova, A. I. Nazarov, V. G. Osmolovskii, N. N. Uraltseva, “A Survey of Results of St. Petersburg State University Research School on Nonlinear Partial Differential Equations. I”, Vestnik St.Petersb. Univ.Math., 57:1 (2024), 1
Bobkov V., Kolonitskii S., “On Qualitative Properties of Solutions For Elliptic Problems With the P-Laplacian Through Domain Perturbations”, Commun. Partial Differ. Equ., 45:3 (2020), 230–252
Bobkov V., Kolonitskii S., “Second-Order Derivative of Domain-Dependent Functionals Along Nehari Manifold Trajectories”, ESAIM-Control OPtim. Calc. Var., 26 (2020), 48
Enin A., “Multiplicity of Positive Solutions For a Critical Quasilinear Neumann Problem”, Arch. Math., 109:3 (2017), 263–272
N. S. Ustinov, “Multiplicity of positive solutions to the boundary value problems for fractional Laplacians”, J. Math. Sci. (N. Y.), 236:4 (2019), 446–460
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
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
A. I. Enin, A. I. Nazarov, “Multiplicity of Solutions to the Quasilinear Neumann Problem in the 3-Dimensional Case”, J Math Sci, 207:2 (2015), 206

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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