Existence of periodic solutions for some second order quasi-linear Hamiltonian systems

Abstract

A class of second order nonautonomous quasilinear Hamiltonian systems $(S)$ is considered. One states that, for any $T<T_0$, depending on the growth coefficients of the Hamiltonian function $H$, there exists a $T$-periodic and $T/2$-antiperiodic solution of $(S)$, in case that two symmetry conditions hold for $H$.