Multiple periodic solutions of Hamiltonian systems in the plane

Abstract

Our aim is to prove a multiplicity result for periodic solutions of Hamiltonian systems in the plane, by the use of the Poincaré-Birkhoff Fixed Point Theorem. Our main theorem generalizes previous results obtained for scalar second order equations by Lazer and McKenna [Large scale oscillatory behaviour in loaded asymmetric systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), 243–274] and Del Pino, Manasevich and Murua [On the number of $2\pi$-periodic solutions for $u''+g(u) =s(1+h(t))$ using the Poincaré–Birkhoff Theorem, J. Differential Equations 95 (1992), 240–258].