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This article is cited in 1 scientific paper (total in 1 paper)
Brief communications
Multiplicity of 1D-concentrated positive solutions to the Dirichlet problem for an equation with $p$-Laplacian
S. B. Kolonitskii St. Petersburg State University, Department of Mathematics and Mechanics
Abstract:
We consider the Dirichlet problem for the equation $-\Delta_p = u^{q-1}$ with $p$-Laplacian in a thin spherical annulus in $\mathbb R^n$ with $1 < p < q < p^*_{n-1}$, where $p^*_{n-1}$ is the critical Sobolev exponent
for embedding in $\mathbb R^{n-1}$ and either $n=4$ or $n \ge 6$. We prove that this problem has a countable set of solutions concentrated in neighborhoods of certain curves. Any two such solutions are nonequivalent if the annulus is thin enough. As a corollary, we prove that the considered problem has as many solutions as required, provided that the annulus is thin enough.
Keywords:
$p$-Laplacian, multiplicity of solutions.
Received: 21.01.2014
Citation:
S. B. Kolonitskii, “Multiplicity of 1D-concentrated positive solutions to the Dirichlet problem for an equation with $p$-Laplacian”, Funktsional. Anal. i Prilozhen., 49:2 (2015), 88–92; Funct. Anal. Appl., 49:2 (2015), 151–154
Linking options:
https://www.mathnet.ru/eng/faa3193https://doi.org/10.4213/faa3193 https://www.mathnet.ru/eng/faa/v49/i2/p88
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Abstract page: | 316 | Full-text PDF : | 138 | References: | 41 | First page: | 27 |
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