Two dimensional elliptic equation

with critical nonlinear growth

Authors:
Takayoshi Ogawa and Takashi Suzuki

Journal:
Trans. Amer. Math. Soc. **350** (1998), 4897-4918

MSC (1991):
Primary 35J60, 35P30, 35J20

DOI:
https://doi.org/10.1090/S0002-9947-98-02269-7

MathSciNet review:
1641254

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the asymptotic behavior of solutions to a semilinear elliptic equation associated with the critical nonlinear growth in two dimensions.

where is a unit disk in and denotes a positive parameter. We show that for a radially symmetric solution of (1.1) satisfies

Moreover, by using the Pohozaev identity to the rescaled equation, we show that for any finite energy radially symmetric solutions to (1.1), there is a rescaled asymptotics such as

locally uniformly in . We also show some extensions of the above results for general two dimensional domains.

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Additional Information

**Takayoshi Ogawa**

Affiliation:
Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106

Address at time of publication:
Graduate School of Mathematics, Kyushu University 36, Fukuoka, 812-8581, Japan

Email:
ogawa@math.kyushu-u.ac.jp

**Takashi Suzuki**

Affiliation:
Department of Mathematics, Osaka University, Toyonaka, Osaka 560, Japan

Email:
takashi@math.sci.osaka-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-98-02269-7

Received by editor(s):
January 29, 1996

Additional Notes:
The first author is on long-term leave from the Graduate School of Polymathematics, Nagoya University, Nagoya 464-01 Japan.

Article copyright:
© Copyright 1998
American Mathematical Society