Resonance in nonlinear discrete systems with nonlinear constraints

In this paper we consider resonant systems of non-linear difference equations subject to nonlinear constraints. The approach used is that of the Alternative Method (Lyapunov-Schmidt Procedure) and results are obtained for the existence of solutions and for their qualitative behavior. These results are extensions of those of Halanay [6] who considered periodic boundary conditions and those of Rodriguez [18] who considered the case of linear homogeneous constraints.