On the discrete version of Picone's identity
For a real number p  with 1<p 1 < p 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 Picone's 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.
05c90 31c45