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Multiple solutions to the Bahri-Coron problem in some domains with nontrivial topology


Authors: Mónica Clapp and Jorge Faya
Journal: Proc. Amer. Math. Soc. 141 (2013), 4339-4344
MSC (2010): Primary 35J66, 35J20
Published electronically: August 28, 2013
MathSciNet review: 3105875
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Abstract: We show that in every dimension $ N\geq 3$ there are many bounded domains $ \Omega \subset \mathbb{R}^{N},$ having only finite symmetries, in which the Bahri-Coron problem

$\displaystyle -\Delta u=\left \vert u\right \vert ^{4/(N-2)}u$$\displaystyle \text { \ in }\Omega ,\text { \ \ }u=0\text { \ on }\partial \Omega ,$

has a prescribed number of solutions, one of them being positive and the rest sign-changing.

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Additional Information

Mónica Clapp
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F., Mexico
Email: monica.clapp@im.unam.mx

Jorge Faya
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F., Mexico
Email: jorgefaya@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-12043-5
Keywords: Nonlinear elliptic boundary value problem, critical exponent, multiple solutions.
Received by editor(s): February 18, 2012
Published electronically: August 28, 2013
Additional Notes: This research was partially supported by CONACYT grant 129847 and PAPIIT-DGAPA-UNAM grant IN106612 (México)
Communicated by: James E. Colliander
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.