Infinitely many sign-changing solutions of an elliptic problem involving critical Sobolev and Hardy-Sobolev exponent

Abstract

We study the existence and multiplicity of sign-changing solutions of the following equation {−Δ𝑢=𝜇|𝑢|2⋆−2𝑢+|𝑢|2∗(𝑡)−2𝑢|𝑥|𝑡+𝑎(𝑥)𝑢inΩ,𝑢=0on∂Ω, where Ω is a bounded domain in ℝ𝑁, 0∈∂Ω, all the principal curvatures of ∂Ω at 0 are negative and μ≥0, a>0, N≥7, 0<t<2, 2⋆=2𝑁𝑁−2 and 2⋆(𝑡)=2(𝑁−𝑡)𝑁−2.