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Positive solutions for elliptic problems with critical nonlinearity and combined singularity

Jianqing ChenEugénio M. Rocha — 2010

Mathematica Bohemica

Consider a class of elliptic equation of the form - Δ u - λ | x | 2 u = u 2 * - 1 + μ u - q in Ω { 0 } with homogeneous Dirichlet boundary conditions, where 0 Ω N ( N 3 ), 0 < q < 1 , 0 < λ < ( N - 2 ) 2 / 4 and 2 * = 2 N / ( N - 2 ) . We use variational methods to prove that for suitable μ , the problem has at least two positive weak solutions.

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