Existence of solutions for a nonlinear algebraic system with a parameter

Taking advantage of a recent critical point theorem, the existence of infinitely many solutionsfor a nonlinear algebraic system with a parameter is established. Our goal was achieved requiring anappropriate behavior of the nonlinear term $f$, either at zero or at infinity, without symmetryconditions. In addition, for a suitable class of systems, a strong discrete maximum principle ispresented.