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.
Unbounded solutions to systems of differential equations at resonance
dambrosio, w;boscaggin, a;papini, d
2022-01-01
Abstract
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.
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