Geodesic
Positive solutions for elliptic problems with critical nonlinearity and combined singularity
Mathematica Bohemica, Tome 135 (2010) no. 4, pp. 413-422

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Consider a class of elliptic equation of the form $$ -\Delta u - {\lambda \over {|x|^2}}u = u^{2^\ast -1} + \mu u^{-q}\quad \mbox {in} \ \Omega \backslash \{0\} $$ with homogeneous Dirichlet boundary conditions, where $0\in \Omega \subset \mathbb R^N$($N\geq 3$), $0 q 1$, $0 \lambda (N-2)^2/4$ and $2^\ast = 2N/(N-2)$. We use variational methods to prove that for suitable $\mu $, the problem has at least two positive weak solutions.
Consider a class of elliptic equation of the form $$ -\Delta u - {\lambda \over {|x|^2}}u = u^{2^\ast -1} + \mu u^{-q}\quad \mbox {in} \ \Omega \backslash \{0\} $$ with homogeneous Dirichlet boundary conditions, where $0\in \Omega \subset \mathbb R^N$($N\geq 3$), $0 q 1$, $0 \lambda (N-2)^2/4$ and $2^\ast = 2N/(N-2)$. We use variational methods to prove that for suitable $\mu $, the problem has at least two positive weak solutions.
DOI : 10.21136/MB.2010.140832
Classification : 35J20, 35J65
Keywords: multiple positive solutions; singular nonlinearity; critical nonlinearity; Hardy term 
Chen, Jianqing; Rocha, Eugénio M. Positive solutions for elliptic problems with critical nonlinearity and combined singularity. Mathematica Bohemica, Tome 135 (2010) no. 4, pp. 413-422. doi: 10.21136/MB.2010.140832
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