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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

   

 

Multiplicity of solutions of the Dirichlet problem for an equation with the $ p$-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: The equation $ -\Delta_p u = 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.


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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