Abstract
In this paper, we use the Linking theorem, Clark theorem and Fountain theorem to obtain the existence of solutions to discrete boundary value problem involving the p-Laplacian on simple, connected, undirected and weighted graphs. We obtain three solutions, infinitely many solutions or a number of solutions depending on a parameter and the number of vertices. The eigenvalues of the nonlinear operator
are concerned in the study.
Acknowledgements
The authors are really grateful to the referee and editor for the useful comments and valuable suggestions which greatly improve the original manuscript.
Notes
No potential conflict of interest was reported by the authors.