Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity

In this paper, we study the existence of ground state sign-changing solutions for following p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity $ {equation*} \{ {}{1.25} {array}{ll} -(a+ b∫ Ω|∇ u|ᵖdx)Δ_p u = |u|q-2uln u^2, ~x∈Ω \\ u = 0, ~\ x∈ ∂Ω, {array} . {equation*} $ where $Ω⊂ RN$ is a smooth bounded domain, $a, b > 0$ are constant, $4≤ 2 p < q < p^*$ and $N > p$. By using constraint variational method, topological degree theory and the quantitative deformation lemma, we prove the existence of ground state sign-changing solutions with precisely two nodal domains.