Abstract :
In the paper we consider the following semilinear elliptic problems with critical Sobolev–Hardy exponents:
⎧⎪
⎨⎪
⎩
− u −
μ
|x|2 u+ λV (x)u = K(x) |u|2∗(s)−2
|x|s
u, in RN,
lim
|x|→∞
u(x) = 0,
(Pμ,s )
where N 3, 0 μ < μ¯ := (N−2
2 )2, λ > 0, 0 s < 2, 2∗(s) = 2(N−s)
N−2 . Under suitable conditions, we prove that (Pμ,s) has
at least one nontrivial solution by means of Linking theorem. Also via the Pseudo-index theory, we consider the multiplicity of
nontrivial solutions for (Pμ,s ).
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