Existence and multiplicity results for boundary value problems connected with the discrete p(·)−p(·)−Laplacian on weighted finite graphs

We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush–Kuhn–Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the discrete p(·)−p(·)−Laplacian on weighted finite graphs. Several auxiliary inequalities for the discrete p(·)−p(·)−Laplacian on finite graphs are also derived. Positive solutions are considered.