## Topological Methods in Nonlinear Analysis

### 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].

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 36, Number 1 (2010), 27-38.

Dates
First available in Project Euclid: 21 April 2016

https://projecteuclid.org/euclid.tmna/1461251062

Mathematical Reviews number (MathSciNet)
MR2744830

Zentralblatt MATH identifier
1221.34111

#### Citation

Fonda, Alessandro; Ghirardelli, Luca. Multiple periodic solutions of Hamiltonian systems in the plane. Topol. Methods Nonlinear Anal. 36 (2010), no. 1, 27--38. https://projecteuclid.org/euclid.tmna/1461251062

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