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 / Boscaggin, A.; Dambrosio, W.; Papini, D.. - In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. - ISSN 1040-7294. - 34:1(2022), pp. 637-650. [10.1007/s10884-020-09890-z]
Unbounded Solutions to Systems of Differential Equations at Resonance
Papini D.
2022
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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BosDamPap_JDDE_2022.pdf
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