Existence and stability of families of periodic solutions in superlinear and sublinear Hamiltonian systems (Q2455303)

The author deals with the Hamiltonian system \[ J\dot x= H_x(t, x),\quad J= \left[\begin{matrix} 0 & -1\\ 1 & 0\end{matrix}\right] \] with \(H(t+ T,x)= H(t, x)\), \(H\in C^2(\mathbb{R}\times \mathbb{R}^{2n}, \mathbb{R})\) or autonomous \((H= H(x))\) Hamiltonian such that \(H_x(t, 0)\equiv 0\), \(H_x(0)= 0\). The author presents nonlocal criteria for the existence and stability of families of periodic solutions emanating from the equilibrium. It is shown that, along such a family, the period changes monotonically.