In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p-Laplacian operator.
D’Aguì, G., Mawhin, J., & Sciammetta, A. (2017). Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian. Journal of Mathematical Analysis and Applications, 447(1), 383-397. https://doi.org/10.1016/j.jmaa.2016.10.023 (Original work published 2017)