Abstract We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity aligned \{ array{ll-, u= |u|^q-2u+| u| ^p ^{*-2}u & in RN, \\ u=0 & on, array. } aligned - Δ γ, p u = λ | u | q - 2 u + u p γ ∗ - 2 u in Ω ⊂ R N, u = 0 on ∂ Ω, where, u: = ₈=₁N Xᵢ (| _ u|^p-2Xᵢ u) Δ γ, p u: = ∑ i = 1 N X i (| ∇ γ u | p - 2 X i u) is the Grushin p -Laplace operator, z: = (x, y) RN
Gandal et al. (Tue,) studied this question.