We deal with a weakly coupled system of ODEs of the type xj′′+nj2xj+hj(x1,...,xd)=pj(t),j=1,...,d,with hj locally Lipschitz continuous and bounded, pj continuous and 2 π-periodic, nj∈ N (so that the system is at resonance). By means of a Lyapunov function approach for discrete dynamical systems, we prove the existence of unbounded solutions, when either global or asymptotic conditions on the coupling terms h1, ... , hd are assumed.
