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math.AP2026
Poisson problem with Hardy operator on lattice graph and the application to semilinear equations
Huyuan Chen, Bobo Hua, Wendi Xu
In this paper, we investigate the analytic properties of the Hardy-type operator on the -dimensional integer lattice graph , where and …
math.AP2025
The Logarithmic Laplacian on General Graphs
Rui Chen, Wendi Xu
We establish, for the first time, a Bochner-type integral representation for the logarithmic Laplacian on weighted graphs. Assuming stochastic completeness of the underlying graph,…
math.AP2023
The existence of ground state solutions for nonlinear p-Laplacian equations on lattice graphs
Bobo Hua, Wendi Xu
In this paper, we study the nonlinear -Laplacian equation with positive and periodic potential on the lattice graph , whe…
math.AP2021
Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs
Bobo Hua, Wendi Xu
In this paper, we study the nonlinear Schrödinger equation on the lattice graph . Using the Nehari method, we prove that when satisfies som…