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Positive solutions for elliptic problems with critical nonlinearity and combined singularity. (English) Zbl 1224.35084
Summary: Consider a class of elliptic equation of the form $-\Delta u - {\lambda \over {| x| ^2}}u = u^{2^{\ast }-1} + \mu u^{-q}\quad \text{in} \;\Omega \backslash \{0\}$ 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.

##### MSC:
 35J20 Variational methods for second-order elliptic equations 35J65 Nonlinear boundary value problems for linear elliptic equations
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