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Asymptotic behavior of solutions to semilinear elliptic equations with Hardy potential

Authors:	Pigong Han

Institution:	Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China

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 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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