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

Abstract In this paper, we study the existence of a ground state solution for the nondegenerate fractional p -Kirchhoff equation $$ \left( \alpha +\beta [u]_{s,p}^p\right) (-\Delta )_p^s u + V(x)|u|^{p-2}u = \lambda a(x)|u|^{q-2}u + |u|^{p_s^*-2}u\,\, \text {in}\,\, \mathbb {R}^N\!, $$ 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 , $$1<p<\!+\infty $$ 1 < p < + ∞ , $$sp<N<2sp$$ s p < N < 2 s p , $$\lambda ,\alpha ,\beta >0$$ λ , α , β > 0 and $$2p<q<p_s^*$$ 2 p < q < p s ∗ . Here $$[u]_{s,p}$$