| Abstract: |
| We study the discrete logarithmic Kirchhoff equation on$\mathbb{Z}^3$:
$$
-\left(a + b \sum_{x \in \mathbb{Z}^3} |\nabla u(x)|^2\right) \Delta u(x) + (\lambda + 1)u(x) = |u|^{p-2}u\log|u|^2,
$$
where$a,b>0$,$p>6$, and$\lambda>0$. By using the Nehari manifold method, we prove the existence of least energy sign-changing solutions under suitable$\lambda$ assumptions. We also analyze their asymptotic behavior as$\lambda\to\infty$ by introducing a limiting equation on bounded domains. Our results extend to$n$-dimensional lattice graphs$\mathbb{Z}^n$, with clear physical motivation from wave propagation and elastic vibration problems. |
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