Remarks on singular critical growth elliptic equations

Shuangjie Peng

doi:10.3934/dcds.2006.14.707

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2006, Volume 14, Issue 4: 707-719. Doi: 10.3934/dcds.2006.14.707

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Remarks on singular critical growth elliptic equations

Shuangjie Peng^1,

1.
School of Mathematics and Statistics, China Central Normal University, Wuhan, 430079

Received: December 31, 2004

Revised: July 31, 2005

Published: September 2006

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Abstract

Let $\Omega$ be a bounded domain in $\mathbb R^N$$(N\geq 4)$ with smooth boundary $\partial \Omega$ and the origin $0 \in \overline{\Omega}$, $\mu<0$, 2^*=2N/(N-2). We obtain existence results of positive and sign-changing solutions to Dirichlet problem $-\Delta u=\mu\frac{ u}{|x|^2}$+|u|^{2^*-2_u}+$\lambda u \ \text{on}\ \Omega,\ u=0 \ \text{on}\ \partial\Omega$, which also gives a positive answer to the open problem proposed by A. Ferrero and F. Gazzola in [Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations, 177(2001), 494-522].

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Mathematics Subject Classification: Primary: 35J60, 35J25; Secondary: 35J33.

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