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Critical semilinear biharmonic equations in RN

Published online by Cambridge University Press:  14 November 2011

Ezzat S. Noussair ,
Charles A. Swanson  and
Yang Jianfu
Ezzat S. Noussair
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia
Charles A. Swanson
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Y4
Yang Jianfu
Affiliation:
Department of Mathematics, Jiangxi University, Nanchang, Jiangxi 330047, People's Republic of China
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Synopsis

An existence theorem is obtained for a fourth-order semilinear elliptic problem in RN involving the critical Sobolev exponent (N + 4)/(N − 4), N>4. A preliminary result is that the best constant in the Sobolev embedding L2N/(N–4) (RN) is attained by all translations and dilations of (1 + ∣x∣2)(4-N)/2. The best constant is found to be

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 1-2 , 1992 , pp. 139 - 148
Copyright
Copyright © Royal Society of Edinburgh 1992

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