Existence of solutions for a nonlinear algebraic system with a parameter

Abstract

Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established. Our goal was achieved requiring an appropriate behavior of the nonlinear term f, either at zero or at infinity, without symmetry conditions. In addition, for a suitable class of systems, a strong discrete maximum principle is presented. © 2012 Elsevier Inc. All rights reserved.