L^p-Parabolicity, the L^q-Liouville Property, and Nonlinear Elliptic Systems on Weighted Graphs

Lu Hao, Yuhua Sun

We establish an equivalence between $L^p$-parabolicity, the $L^q$-Liouville property for nonnegative superharmonic functions, and the rigidity of nonnegative solutions to the ellip…