MULTIPLE POSITIVE SOLUTIONS FOR DISCRETE p-LAPLACIAN EQUATIONS WITH POTENTIAL TERM.

We study the existence of solutions to nonlinear discrete boundary value problems with the discrete p-Laplacian, potential, and nonlinear source terms. Using variational methods, we demonstrate that there exist at least two positive solutions. The existence strongly depends on the smallest positive eigenvalue of Dirichlet eigenvalue problems and the growth conditions of the source terms. [ABSTRACT FROM AUTHOR]