On the weighted elliptic problems involving multi-singular potentials and multi-critical exponents |
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Authors: | Dong Sheng Kang |
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Institution: | (1) Department of Mathematics, South-Central University for Nationalities, Wuhan, 430074, P. R. China |
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Abstract: | Suppose Ω ⊂ ℝ
N
(N ≥ 3) is a smooth bounded domain, and are the weighted critical Hardy-Sobolev exponents, i = 1, 2,…, k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical
elliptic problem with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality.
The results depend crucially on the parameters a
i
, b
i and μ
i
, i = 1, 2,…, k.
This work is supported partly by the National Natural Science Foundation of China (10771219) and the Science Foundation of
the SEAC of China (07ZN03) |
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Keywords: | multi-singular multi-critical weighted elliptic problem weighted Hardy-Sobolev exponent |
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