On G-symmetric solutions of a quasilinear elliptic equation involving critical Hardy–Sobolev exponent
- Deng, Zhiying
- Huang, Yisheng
DOIAbstract
AbstractThis paper deals with the class of singular quasilinear elliptic problem−Δpu=μ|u|p−2u|x|p+k(x)|u|p⁎(s)−2u|x|s+λf(x,u)in Ω,u=0on ∂Ω, where Ω⊂RN is a smooth bounded domain, and Ω is G-symmetric with respect to a subgroup G of O(N), 0∈Ω, 1<p<N, Δpu=div(|∇u|p−2∇u) is the p-Laplacian, 0⩽μ<μ¯, μ¯=(N−pp)p, 0⩽s<p, λ⩾0, p⁎(s)=(N−s)pN−p, k(x) is continuous and G-symmetric on Ω¯, and f:Ω×R↦R is a continuous nonlinearity of lower order satisfying some conditions. By using the variational methods and analytic techniques, we obtain several existence and multiplicity results of G-symmetric solutions under certain hypotheses on μ, λ and k
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