Multiplicity of solutions of the Dirichlet problem for an equation with the -Laplacian in a three-dimensional spherical layer

Author:
S. B. Kolonitskiĭ

Translated by:
N. B. Lebedinskaya

Original publication:
Algebra i Analiz, tom **22** (2010), nomer 3.

Journal:
St. Petersburg Math. J. **22** (2011), 485-495

MSC (2010):
Primary 35J92

Published electronically:
March 18, 2011

MathSciNet review:
2729947

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Abstract | References | Similar Articles | Additional Information

Abstract: The equation 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.

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Additional Information

**S. B. Kolonitskiĭ**

Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, 28 Universitetskii Prospekt, Peterhoff, St. Petersburg 198504, Russia

Email:
sergey.kolonitskii@gmail.com

DOI:
http://dx.doi.org/10.1090/S1061-0022-2011-01154-9

Keywords:
$p$-Laplacian,
existence of many solutions

Received by editor(s):
September 22, 2009

Published electronically:
March 18, 2011

Additional Notes:
Supported by RFBR (grant no. 08-01-00748) and by the grant NSh–227.2008.1 for support of leading scientific schools

Article copyright:
© Copyright 2011
American Mathematical Society