Ground states for critical fractional p-Laplacian Kirchhoff-type problems

In this paper, we study the existence of a ground state solution for the nondegenerate fractional p -Kirchhoff equation ( α +β [u]s,pᵖ) (-Δ )ₚˢ u + V(x)|u|ᵖ⁻²u = λ a(x)|u|q-2u + |u|pₛ^*-2u\,\, in\,\, RN\!, α + β [ u ] s , p p ( - Δ ) p s u + V ( x ) | u | p - 2 u = λ a ( x ) | u | q - 2 u + | u | p s ∗ - 2 u in R N , where $$0<s<1$$ 0 < s < 1 , 1<p<\!+∞ 1 < p < + ∞ , $$sp<N<2sp$$ s p < N < 2 s p , λ ,α ,β >0 λ , α , β > 0 and 2p<q<pₛ^* 2 p < q < p s ∗ . Here [u]s,p