Alexander Grigorʼyan

6 citations · 6 across the 4 of their papers we have counts for

collaborators

4 papers

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…

math.AT2014★ 6 cited

Homotopy theory for digraphs

Alexander Grigor'yan, Yong Lin, Yuri Muranov +1

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors i…

math.DG2014

A lower bound for the number of negative eigenvalues of Schrödinger operators

Alexander Grigor'yan, Nikolai Nadirashvili, Yannick Sire

We prove a lower bound for the number of negative eigenvalues for a Schrödinger operator on a Riemannian manifold via the integral of the potential.