Solutions to critical elliptic equations with multi-singular inverse square potentials

@inproceedings{Cao2006SolutionsTC,
  title={Solutions to critical elliptic equations with multi-singular inverse square potentials},
  author={Daomin Cao and Pigong Han},
  year={2006}
}
Abstract Let Ω be an open-bounded domain in R N ( N ⩾ 3 ) with smooth boundary ∂ Ω . We are concerned with the multi-singular critical elliptic problem - Δ u - ∑ i = 1 k μ i u | x - a i | 2 = Q ( x ) | u | 2 * - 2 u , u ∈ H 0 1 ( Ω ) , ( * ) where μ i ∈ R , 2 * = 2 N N - 2 , a i ∈ Ω ( 1 ⩽ i ⩽ k ) and Q ( x ) is a positive bounded function on Ω ¯ . Using Moser iteration, we prove the asymptotic behavior of solutions for ( * ) at points a i ( 1 ⩽ i ⩽ k ) . By exploiting the effect of the… CONTINUE READING

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