We study some semi-linear equations for the (m,p)-Laplacian operator on
locally finite weighted graphs. We prove existence of weak solutions for all
mβN and pβ(1,+β) via a variational method already known
in the literature by exploiting the continuity properties of the energy
functionals involved. When m=1, we also establish a uniqueness result in the
spirit of the Brezis-Strauss Theorem. We finally provide some applications of
our main results by dealing with some Yamabe-type and Kazdan-Warner-type
equations on locally finite weighted graphs.Comment: 13 page