On the Solvability of the Discrete s(x, .)-Laplacian Problems on Simple, Connected, Undirected, Weighted, and Finite Graphs

We use the finite dimensional monotonicity methods in order to investigate problems connected with the discrete s (x , .)-Laplacian on simple, connected, undirected, weighted, and finite graphs with nonlinearities given in a non-potential form. Positive solutions are also considered.

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We utilize finite dimensional monotonicity methods to investigate problems related to the discrete s(x,.)-Laplacian on simple, connected, undirected, weighted, and finite graphs with nonlinearities given in a non-potential form. Positive solutions are also taken into consideration.