Nontrivial periodic solutions for strong resonance Hamiltonian systems
A nonautonomous Hamiltonian system of the form \[ -J{dx\over dt}= H_x(t,x), \] where \(H\in C^2([0,1]\times \mathbb{R}^{2n},\mathbb{R})\) is 1-periodic in \(t\) and \[ J=\begin{pmatrix} 0 & -I_n\\ I_n & 0\end{pmatrix} \] is considered. Under the assumption that the Hamiltonian has an asymptotically linear gradient and the linearized operators have distinct Maslov indices at \(0\) and at infinity it is proved the existence of nontrivial periodic solutions.
scientific article; zbMATH DE number 1019547
scientific article