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A global compactness result for singular elliptic problems involving critical Sobolev exponent


Authors: Daomin Cao and Shuangjie Peng
Journal: Proc. Amer. Math. Soc. 131 (2003), 1857-1866
MSC (2000): Primary 35J60; Secondary 35B33
DOI: https://doi.org/10.1090/S0002-9939-02-06729-1
Published electronically: October 1, 2002
MathSciNet review: 1955274
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Abstract: Let $\Omega \subset R^N $ be a bounded domain such that $0 \in \Omega, N \geq 3,2^*=\frac{2N}{N-2},\lambda \in R, \epsilon \in R $. Let $\{u_n\}\subset H_0^1(\Omega)$ be a (P.S.) sequence of the functional $E_{\lambda,\epsilon}(u)=\frac{1}{2}\int_{\Omega}(\vert\nabla u\vert^{2}-\frac{\... ...^2}{\vert x\vert^2}-\epsilon u^2)-\frac{1}{2^*}\int_{\Omega} \vert u\vert^{2^*}$. We study the limit behaviour of $u_n$ and obtain a global compactness result.


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Additional Information

Daomin Cao
Affiliation: Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: dmcao@mail.amt.ac.cn

Shuangjie Peng
Affiliation: Department of Mathematics, Xiao Gan University, Xiao Gan, People’s Republic of China – and – Institute of Applied Mathematics, AMSS., Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: pengsj@mail.amss.ac.cn

DOI: https://doi.org/10.1090/S0002-9939-02-06729-1
Keywords: Palais-Smale sequence, compactness, Sobolev and Hardy critical exponents
Received by editor(s): December 2, 2001
Received by editor(s) in revised form: January 31, 2002
Published electronically: October 1, 2002
Additional Notes: The first author was supported by Special Funds For Major States Basic Research Projects of China (G1999075107) and Knowledge Innovation Funds of CAS in China.
The second author was supported by Knowledge Innovation Funds of CAS in China
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society

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