A. Grigor’yan

activity

20102026

most citedExistence of positive solutions to some nonlinear equations on locally finite graphs

108 citations · 294 across the 20 of their papers we have counts for

collaborators

Showing 2016 · math.APShow all

3 papers · 2 filters

math.AP2016★ 108 cited

Existence of positive solutions to some nonlinear equations on locally finite graphs

Alexander Grigor'yan, Yong Lin, Yunyan Yang

Let $G = (V, E)$ be a locally finite graph, whose measure $μ (x)$ have positive lower bound, and $Δ$ be the usual graph Laplacian. Applying the mountain-pass theorem due to Ambrosetti-…

math.AP2016

Kazdan-Warner equation on graph

Alexander Grigor'yan, Yong Lin, Yunyan Yang

Let $G = (V, E)$ be a finite graph and $Δ$ be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various conditions such th…

math.AP2016

Yamabe type equations on graphs

Alexander Grigor'yan, Yong Lin, Yunyan Yang

Let $G = (V, E)$ be a locally finite graph, $Ω \subset V$ be a bounded domain, $Δ$ be the usual graph Laplacian, and $λ_{1} (Ω)$ be the first eigenvalue of $- Δ$ with respect to Dirichlet…