Open AccessSubharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth
Author(s) -
Fanfan Chen,
Dianwei Qian,
Xiaoxiao Sun,
WU Yin-yin
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021180
Subject(s) - sublinear function , bounded function , mathematics , hamiltonian system , eigenvalues and eigenvectors , subharmonic , multiplicity (mathematics) , mathematical analysis , pure mathematics , twist , hamiltonian (control theory) , scalar (mathematics) , mathematical physics , physics , nonlinear system , quantum mechanics , geometry , mathematical optimization
We prove the existence and multiplicity of subharmonic solutions for bounded coupled Hamiltonian systems. The nonlinearities are assumed to satisfy Landesman-Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is based on phase plane analysis and a higher dimensional version of the Poincaré-Birkhoff twist theorem by Fonda and Ureña. The results obtained generalize the previous works for scalar second-order differential equations or relativistic equations to higher dimensional systems.