We study the existence of solutions to nonlinear discrete boundary value prob- lems with the discrete p-Laplacian, potential, and nonlinear source terms. Us- ing variational methods, we demonstrate that there exist at least two positive solutions. The existence strongly depends on the smallest positive eigenvalue of Dirichlet eigenvalue problems and the growth conditions of the source terms.
- Discrete boundary value problems
- Discrete p-Laplacian
- Graph Laplacian
- Multiple solutions