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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multiple solutions for elliptic problems with singular and sublinear potentials


Authors: Alexandru Kristály and Csaba Varga
Journal: Proc. Amer. Math. Soc. 135 (2007), 2121-2126
MSC (2000): Primary 35J60, 35J65
Published electronically: February 6, 2007
MathSciNet review: 2299489
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Abstract: For certain positive numbers $ \mu$ and $ \lambda,$ we establish the multiplicity of solutions to the problem

\begin{displaymath}\left\{ \begin{array}{lll} -\triangle u=\mu\frac{u}{\vert x\v... ... \Omega,\\ u=0 & {\rm on} \partial \Omega, \end{array}\right. \end{displaymath}

where $ \Omega$ is a bounded open domain in $ \mathbb{R}^N (N\geq 3)$ containing the origin with smooth boundary $ \partial \Omega,$ while $ f:\mathbb{R}\to\mathbb{R}$ is continuous, superlinear at zero and sublinear at infinity.


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Additional Information

Alexandru Kristály
Affiliation: University of Babeş-Bolyai, Faculty of Economics, Str. Teodor Mihali 58-60, RO-400591, Cluj Napoca, Romania
Email: alexandrukristaly@yahoo.com

Csaba Varga
Affiliation: University of Babeş-Bolyai, Faculty of Mathematics and Computer Science, Str. Kogalniceanu 1, RO-400084, Cluj-Napoca, Romania
Email: csvarga@math.ubbcluj.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08715-1
PII: S 0002-9939(07)08715-1
Keywords: Singular potential, sublinearity at infinity, multiple solutions
Received by editor(s): November 29, 2005
Received by editor(s) in revised form: March 15, 2006
Published electronically: February 6, 2007
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.