Abstract We investigate the existence and multiplicity of solutions for a class of the generalized coupled system involving poly-Laplacian and the parameter λ on finite graphs. By using the Mountain pass lemma together with the cut-off technique, we obtain that system has at least a nontrivial weak solution (u λ, v λ) (u, v) for every large parameter λ when the nonlinear term F (x, u, v) F (x, u, v) satisfies superlinear growth conditions only in a neighborhood of origin point (0, 0). We also obtain a concrete form for the lower bound of λ and the trend of (u λ, v λ) (u, v) with the change of λ. Moreover, by using a revised Clark’s theorem together with cut-off technique, we obtain that system has a sequence of solutions tending to 0 for every λ > 0 0 when the nonlinear term F (x, u, v) F (x, u, v) satisfies sublinear growth conditions only in a neighborhood of origin point (0, 0).
Qi et al. (Wed,) studied this question.