Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations

In this paper, we study the discrete fractional logarithmic Kirchhoff equation $$(a+b{\int }_{{\mathbb{Z}}^d}\mathrm{\mid }{\mathrm{\nabla }}^{s}u{\mathrm{\mid }}^{2}d\mu )(-\mathrm{\Delta }{)}^{s}u+h(x)u=\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u\log u^2,x\in {\mathbb{Z}}^d,$$ where $a,b>0$ and $0<s<1$. Under suitable assumptions on $h(x)$, we first prove the existence of ground state solutions by the mountain-pass theorem for $p>4$; then we verify the existence of ground state sign-changing solutions based on the method of Nehari manifold for $p>6$. Finally, we establish the multiplicity of nontrivial weak solutions.