Mengqiu Shao

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math.AP2023

Sobolev spaces on locally finite graphs

Mengqiu Shao, Yunyan Yang, Liang Zhao

In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exac…

math.AP2023

Existence and convergence of solutions to $p$ -Laplace equations on locally finite graphs

Mengqiu Shao, Yunyan Yang, Liang Zhao

We are mainly concerned with the nonlinear $p$ -Laplace equation \begin{equation*} -Δ_pu+ρ|u|^{p-2}u=ψ(x,u) \end{equation*} on a locally finite graph $G = (V, E)$ , where $p$ belongs to…

math.AP2019

Existence and convergence of solutions for nonlinear biharmonic equations on graphs

Xiaoli Han, Mengqiu Shao, Liang Zhao

In this paper, we first prove some propositions of Sobolev spaces defined on a locally finite graph $G = (V, E)$ , which are fundamental when dealing with equations on graphs under the…

Sobolev spaces on locally finite graphs

Existence and convergence of solutions to p-Laplace equations on locally finite graphs

Existence and convergence of solutions for nonlinear biharmonic equations on graphs

Existence and convergence of solutions to $p$ -Laplace equations on locally finite graphs