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October  2006, 14(4): 707-719. doi: 10.3934/dcds.2006.14.707

Remarks on singular critical growth elliptic equations

Shuangjie Peng 1,

1. 

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

Received  January 2005 Revised  August 2005 Published  January 2006

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*-2u+$\lambda u \ \text{on}\ \Omega,\ u=0 \ \text{on}\ \partial\Omega$, 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].
Keywords: Hardy inequality, singular elliptic equation., critical Sobolev exponents, Positive and sign-changing solutions, compactness.
Mathematics Subject Classification: Primary: 35J60, 35J25; Secondary: 35J3.
Citation: Shuangjie Peng. Remarks on singular critical growth elliptic equations. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 707-719. doi: 10.3934/dcds.2006.14.707
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