Unbounded solutions to systems of differential equations at resonance

Abstract

We deal with a weakly coupled system of ODEs of the typewith hj locally Lipschitz continuous and bounded, pj continuous and 2π-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, . . . , h d are assumed.