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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Single-point condensation
and least-energy solutions


Authors: Xiaofeng Ren and Juncheng Wei
Journal: Proc. Amer. Math. Soc. 124 (1996), 111-120
MSC (1991): Primary 35B40, 35A08, 35A15; Secondary 34A34
MathSciNet review: 1301045
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a conjecture raised in our earlier paper which says that the least-energy solutions to a two-dimensional semilinear problem exhibit single-point condensation phenomena as the nonlinear exponent gets large. Our method is based on a sharp form of a well-known borderline case of the Sobolev embedding theory. With the help of this embedding, we can use the Moser iteration scheme to carefully estimate the upper bound of the solutions. We can also determine the location of the condensation points.


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Additional Information

Xiaofeng Ren
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Institute for Mathematics & Applications, University of Minnesota, Minneapolis, Minnesota 55455
Email: ren@ima.umn.edu

Juncheng Wei
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03156-5
PII: S 0002-9939(96)03156-5
Received by editor(s): July 2, 1994
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1996 American Mathematical Society