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Asymptotic behavior of solutions to semilinear elliptic equations with Hardy potential

Author: Pigong Han
Journal: Proc. Amer. Math. Soc. 135 (2007), 365-372
MSC (2000): Primary 35J65, 58E05
Published electronically: August 1, 2006
MathSciNet review: 2255282
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Abstract: Let $ \Omega$ be an open bounded domain in $ \mathbb{R}^N (N\geq3)$ with smooth boundary $ \partial\Omega$, $ 0\in\Omega$. We are concerned with the asymptotic behavior of solutions for the elliptic problem:

$\displaystyle (*)\qquad\qquad\qquad -\Delta u-\frac{\mu u}{\vert x\vert^2}=f(x, u),\qquad\,\,u\in H^1_0(\Omega),\qquad\qquad\qquad\qquad \ $

where $ 0\leq\mu<\big(\frac{N-2}{2}\big)^2$ and $ f(x, u)$ satisfies suitable growth conditions. By Moser iteration, we characterize the asymptotic behavior of nontrivial solutions for problem $ (*)$. In particular, we point out that the proof of Proposition 2.1 in Proc. Amer. Math. Soc. 132 (2004), 3225-3229, is wrong.

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Pigong Han
Affiliation: Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China

Received by editor(s): April 8, 2005
Received by editor(s) in revised form: August 11, 2005
Published electronically: August 1, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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