Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator

Partial difference equations have received more and attention in recent years due to their extensive applications diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial equation involving mean curvature operator. By applying critical point theory, existence at least three solutions is obtained. Furthermore, under some appropriate assumptions on nonlinearity, respectively show that admits two or positive by means strong maximum principle. Finally, present concrete examples combine with images illustrate our main results.