Ground state sign-changing solution for a logarithmic Kirchhoff-type equation in R 3

Abstract

We investigate the following logarithmic Kirchhoff-type equation: ( a + b ∫ R 3 | ∇ u | 2 + V ( x ) u 2 d x ) [ − Δ u + V ( x ) u ] = | u | p − 2 u ln ⁡ | u | , x ∈ R 3 , where a , b > 0 are constants, 4 < p < 2 ∗ = 6 . Under some appropriate hypotheses on the potential function V , we prove the existence of a positive ground state solution, a ground state sign-changing solution and a sequence of solutions by using the constraint variational methods, topological degree theory, quantitative deformation lemma and symmetric mountain pass theorem. Our results complete those of Gao et al. [Appl. Math. Lett. 139(2023), 108539] with the case of 4 < p < 6 .