The minimal period problem for nonconvex even second order Hamiltonian systems (Q1378579)

The authors consider classical Hamiltonian systems \[ \ddot x + V'(x)=0 , \qquad \forall\;x\in \mathbb{R}^N \] with \(V\in C^2({\mathbb{R}}^N,{\mathbb{R}})\) and \[ V(x)={1\over 2} h_0x\cdot x+\widetilde VB(x) , \qquad \forall\;x\in{\mathbb{R}}^N , \] with \(h_0\in {{\mathcal L}}_s({\mathbb{R}}^N)\), \(x\cdot x\) is the inner product, \(\widetilde V\) is even, \(\widetilde V(-x)=\widetilde V(x)\), \(\forall\;x\in{\mathbb{R}}^N\) and \(\widetilde V(x)=o(| x| ^2) \) as \(| x| \to 0\). By using variational methods, they obtain estimates for the minimal period of the corresponding nonconstant periodic solutions to superquadratic and asymptotically linear Hamiltonian systems.