  This work is devoted to the study of the existence of at least one (non-zero)
solution to a problem involving the discrete $p$-Laplacian. As a special case,
we derive an existence theorem for a second-order discrete problem, depending
on a positive real parameter $\alpha$, whose prototype is given by $$ \left\{
\begin{array}{l} -\Delta^2u({k-1})=\alpha f(k,u(k)),\quad \forall\; k \in
{\mathbb{Z}}[1,T] \\ {u(0)=u({T+1})=0.}\\ \end{array} \right. $$ Our approach
is based on variational methods in finite-dimensional setting.
