Critical point theory to isotropic discrete boundary value problems on weighted finite graphs
Qiang Huo, Yu Tian, Tengteng Ma · The Journal of Difference Equations and Applications · 2018
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 λ and the number of vertices. The eigenvalues of the nonlinear operator -Δp,ω+q are concerned in the study.