Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs

Abstract We investigate a generalized poly-Laplacian system with a parameter on weighted finite graphs, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a (p, q) (p, q) -Laplacian system with a parameter on weighted locally finite graphs. We utilize a critical points theorem built by Bonanno and Bisci Bonanno, Bisci, and Regan, Math. Comput. Model. 52 (1-2): 152–160, 2010, which is an abstract critical points theorem without compactness condition, to obtain that these systems have infinitely many nontrivial solutions with unbounded norm when the parameters locate some well-determined range.