On the elliptic problems involving multi-singular inverse square potentials and critical Sobolev exponent

Assume that Ω ⊂ R N ( N ≥ 3 ) is a smooth bounded domain, a i are different points in Ω , i = 1 , 2 , … , k , k ≥ 2 , λ > 0 , 2 ≤ q < 2 ∗ , μ < μ ̄ ≔ ( N − 2 2 ) 2 , 2 ∗ = 2 N N − 2 is the critical Sobolev exponent. We study the existence and asymptotic behavior of solutions to the multi-si...

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Veröffentlicht in:Nonlinear analysis 2008-05, Vol.68 (10), p.3050-3066
1. Verfasser: Kang, Dongsheng
Format: Artikel
Sprache:eng
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Zusammenfassung:Assume that Ω ⊂ R N ( N ≥ 3 ) is a smooth bounded domain, a i are different points in Ω , i = 1 , 2 , … , k , k ≥ 2 , λ > 0 , 2 ≤ q < 2 ∗ , μ < μ ̄ ≔ ( N − 2 2 ) 2 , 2 ∗ = 2 N N − 2 is the critical Sobolev exponent. We study the existence and asymptotic behavior of solutions to the multi-singular critical elliptic problem − Δ u − μ u ∏ i = 1 k | x − a i | 2 = | u | 2 ∗ − 2 u + λ | u | q − 2 u with Dirichlet boundary condition. The results depend crucially on the parameters λ , μ and q .
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2007.01.073