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

DOI:
https://doi.org/10.1090/S0002-9939-96-03156-5

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:
https://doi.org/10.1090/S0002-9939-96-03156-5

Received by editor(s):
July 2, 1994

Communicated by:
Jeffrey Rauch

Article copyright:
© Copyright 1996
American Mathematical Society