On stable entire solutions of semilinear elliptic equations with weights
Authors:
Craig Cowan and Mostafa Fazly
Journal:
Proc. Amer. Math. Soc. 140 (2012), 20032012
MSC (2010):
Primary 35B08; Secondary 35J61, 35A01
Published electronically:
September 30, 2011
MathSciNet review:
2888188
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Additional Information
Abstract: We are interested in the existence versus nonexistence of nontrivial stable sub and supersolutions of  (1)  with positive smooth weights . We consider the cases where and where . We obtain various nonexistence results which depend on the dimension and also on and the behaviour of near infinity. Also the monotonicity of is involved in some results. Our methods here are the methods developed by Farina. We examine a specific class of weights and , where is a positive function with a finite limit at . For this class of weights, nonexistence results are optimal. To show the optimality we use various generalized Hardy inequalities.
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Additional Information
Craig Cowan
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
Email:
ctcowan@stanford.edu
Mostafa Fazly
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2
Email:
fazly@math.ubc.ca
DOI:
http://dx.doi.org/10.1090/S000299392011113510
Keywords:
Semilinear elliptic equations,
Hardy’s inequality,
stable solutions
Received by editor(s):
February 3, 2011
Published electronically:
September 30, 2011
Additional Notes:
This work is supported by a University Graduate Fellowship and is part of the second author’s Ph.D. dissertation in preparation under the supervision of N. Ghoussoub.
Communicated by:
James E. Colliander
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
