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Complex Variables and Elliptic Equations
An International Journal
Volume 57, 2012 - Issue 11: Critical Point Theory and Elliptic Problems
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Original Articles

Sign-changing and symmetry-breaking solutions to singular problems

Andrzej Szulkin Department of Mathematics, Stockholm University, 106 91 Stockholm, SwedenCorrespondence[email protected]
&
Shoyeb Waliullah Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
Pages 1191-1208 | Received 30 Apr 2010, Accepted 23 Jun 2010, Published online: 02 Feb 2011
 
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Abstract

We consider the degenerate elliptic equation

related to the Caffarelli–Kohn–Nirenberg inequality. We show that it possesses infinitely many solutions which are sign-changing and nonradial. The solutions are obtained by constrained minimization on subspaces consisting of functions which have certain prescribed symmetry properties. We also extend these results to higher order equations.

AMS Subject Classifications::

Acknowledgements

Shoyeb Waliullah was supported in part by a grant from the Magnuson Foundation.

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