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arXiv · 2508.18840

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations

Lidan Wang
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Abstract

In this paper, we study the discrete fractional logarithmic Kirchhoff equation $$ \left(a+b \int_{\mathbb{Z}^d}|\nabla^s u|^{2} d μ\right) (-Δ)^s u+h(x) u=|u|^{p-2}u \log u^{2}, \quad x\in \mathbb{Z}^d, $$ where $a,\,b>0$ and $0 4$; 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.

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Lidan Wang. 2025-08-26. Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations. https://arxiv.org/abs/2508.18840

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