Ground states for logarithmic Schrödinger equations on locally finite graphs

Xiaojun Chang, Ru Wang, Duokui Yan

In this paper, we study the following logarithmic Schrödinger equation \[ -Δu+a(x)u=u\log u^2\ \ \ \ \mbox{in }V, \] where $\Delta$ is the graph Laplacian, $G=(V,E)$ is a connected loca…