Planar Hamiltonian systems at resonance: the Ahmad-Lazer-Paul condition (Q354399)

The authors consider a planar Hamiltonian system. By means of an Ahmad-Lazer-Paul type condition, they 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 authors also analyze the relationship of an Ahmad-Lazer-Paul type condition with the Landesman-Lazer condition.