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We prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincaré–Birkhoff fixed point theorem.
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Alberto Boscaggin, Periodic solutions to superlinear planar Hamiltonian systems. Port. Math. 69 (2012), no. 2, pp. 127–140DOI 10.4171/PM/1909