We investigate the existence of three solutions for a partial discrete Dirichlet problem of the Kirchhoff type involving p-Laplacian. This study represents the first systematic attempt to address such a problem in the context of discrete systems. Through rigorous analysis, we establish the existence of at least three distinct solutions under appropriate conditions. The theoretical findings are substantiated with one illustrative example.

Large constant-sign solutions for boundray value problems (Bvps) of the partial discrete difference equation involving ( p,q)-Laplacian is investigated in this paper. The method is based on the critical point theory and truncation techniques. Even reducing to the ordinary difference equations, our results generalize and significantly improve some existing ones. In the end, the obtained results are exemplified based on two examples.