Sign-changing solutions to discrete nonlinear logarithmic Kirchhoff equations

Abstract

In this paper, we study the discrete logarithmic Kirchhoff equation $$-\left(a+b{\int }_{{\mathbb{Z}}^3}|\nabla u{|}^{2}d\mu \right)\Delta u+(\lambda h(x)+1)u=|u{|}^{p-2}u\log u^2,x\in {\mathbb{Z}}^3,$$ where $a,b>0,p>6$ and $\lambda$ is a positive parameter. Under suitable assumptions on $h(x)$, we prove the existence and asymptotic behavior of least energy sign-changing solutions for the equation by the method of Nehari manifold.

24 pages