Abstract
We consider the planar Hamiltonian system
with F(u) positive and positively 2-homogeneous and \({\nabla_{u}R(t, u)}\) sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman–Lazer condition is analyzed, as well.
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With our warmest wishes to Professor Fabio Zanolin for his 60th birthday.
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Boscaggin, A., Garrione, M. Planar Hamiltonian systems at resonance: the Ahmad–Lazer–Paul condition. Nonlinear Differ. Equ. Appl. 20, 825–843 (2013). https://doi.org/10.1007/s00030-012-0181-2
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DOI: https://doi.org/10.1007/s00030-012-0181-2