Mengqiu Shao
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View article: Global existence and multiplicity of solutions for logarithmic Schrödinger equations on graphs
Global existence and multiplicity of solutions for logarithmic Schrödinger equations on graphs Open
We consider the following logarithmic Schrödinger equation $$ -Δu+h(x)u=u\log u^{2} $$ on a locally finite graph $G=(V,E)$, where $Δ$ is a discrete Laplacian operator on the graph, $h$ is the potential function. Different from the classica…
View article: Calculus of variations on hypergraphs
Calculus of variations on hypergraphs Open
We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function spaces on hypergraphs. Several results related to the maxi…
View article: Sobolev spaces on locally finite graphs
Sobolev spaces on locally finite graphs Open
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 exact concept of dimension on graphs, classical methods that wo…