Convergence of ground state solutions for nonlinear Schrödinger equations on graphs

Ning Zhang, Liang Zhao

We consider the nonlinear Schrödinger equation $-\Delta u+(\lambda a(x)+1)u=|u{|}^{p-1}u$ on a locally finite graph $G=(V,E)$. We prove via the Nehari method that if $a(x)$ satisfies certain assu…