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 …

Abstract Let G=(V, E) G=(V, E) be a finite or locally finite connected weighted graph, Δ Δ be
the usual graph Laplacian. Using heat kernel estimates, we prove the existence and …

Discrete time random walks on a finite set naturally translate via a one-to-one
correspondence to discrete Laplace operators. Typically, Ollivier curvature has been …

We consider the nonlinear Schrödinger equation-Δ u+(λ a (x)+ 1) u=| u| p-1 u on a locally
finite graph G=(V, E). We prove via the Nehari method that if a (x) satisfies certain …

We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed
by solving a linear system of equations. We show that graphs with curvature bounded below …

We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature
bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex …

Let (V, E) be a finite connected graph. We are concerned about the Chern–Simons Higgs
model 0.1 Δ u= λ eu (eu-1)+ f, where Δ is the graph Laplacian, λ is a real number and f is a …

Abstract Let G=(V, E) be a locally finite, connected and weighted graph. We prove that, for a
graph satisfying curvature dimension condition CDE′(n, 0) and uniform polynomial volume …

In this paper, we focus on the theory of Sobolev spaces on locally finite graphs, including
completeness, reflexivity, separability and Sobolev inequalities. We introduce a linear space …

We introduce a Laplacian separation principle for the the eikonal equation on Markov
chains. As application, we prove an isoperimetric concentration inequality for Markov chains …