On the discrete version of Piconeʹs identity Original Research Article

For a real number p with image we consider the first eigenvalues of the p-Laplacian on graphs, and estimates for the solutions of p-Laplace equations on graphs. We provide a discrete version of Piconeʹs identity and its application. More precisely, we prove a Barta-type inequality for graphs with boundary. Finally, we provide a discrete version of the anti-maximum principle.