On the classification of solutions of on : Stability outside a compact set and applications

Authors:
E. N. Dancer and Alberto Farina

Journal:
Proc. Amer. Math. Soc. **137** (2009), 1333-1338

MSC (2000):
Primary 35J60, 35B05, 35J25, 35B32

DOI:
https://doi.org/10.1090/S0002-9939-08-09772-4

Published electronically:
December 4, 2008

MathSciNet review:
2465656

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this short paper we prove that, for , the problem on the entire Euclidean space does not admit any solution stable outside a compact set of . This result is obtained without making any assumption about the boundedness of solutions. Furthermore, as a consequence of our analysis, we also prove the non-existence of finite Morse Index solutions for the considered problem. We then use our results to give some applications to bounded domain problems.

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Additional Information

**E. N. Dancer**

Affiliation:
School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia

Email:
normd@maths.usyd.edu.au

**Alberto Farina**

Affiliation:
LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, Faculté de Mathématiques et d’Informatique, 33, rue Saint-Leu, 80039 Amiens, France

Email:
alberto.farina@u-picardie.fr

DOI:
https://doi.org/10.1090/S0002-9939-08-09772-4

Received by editor(s):
November 8, 2007

Published electronically:
December 4, 2008

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2008
American Mathematical Society