On the elliptic problems involving multi-singular inverse square potentials and multi-critical Sobolev–Hardy exponents

✍ Scribed by Dongsheng Kang; Guiqing Li

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 197 KB
• Volume: 66
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.02.026

✦ Synopsis

Let Ω ⊂ R N (N ≥ 3) be a smooth bounded domain such that the different points

, are the critical Sobolev-Hardy exponents. We deal with the conditions that ensure the existence of positive solutions for the multi-singular and multi-critical elliptic problem

with the Dirichlet boundary condition, involving the Hardy inequality and the Sobolev-Hardy inequality. The results depend crucially on the parameters s i and μ i , i = 1, 2, . . . , k.