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Original Articles

Sign-changing and symmetry-breaking solutions to singular problems

&
Pages 1191-1208 | Received 30 Apr 2010, Accepted 23 Jun 2010, Published online: 02 Feb 2011
 

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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