Periodic and subharmonic solutions for a class of superquadratic Hamiltonian systems
The authors prove two existence theorems for periodic solutions of a Hamiltonian system of the form \[ -J \dot{u}=\nabla H(t,u), \] where \(u \in \mathbb R^{2n}\), \(J\) is the symplectic matrix and \(H\) a Hamiltonian function \(T\)-periodic in \(t\). In the first theorem, under some conditions on \(H\), they show the existence of at least one nontrivial \(T\)-periodic solution. In the second theorem, they show the existence of infinitely many subharmonic solutions. In their proofs, they use the generalized mountain pass theorem and a theorem due to \textit{S. Li} and \textit{A. Shujie} [J. Differ. Equations 112, No.1, 226-238 (1994; Zbl 0807.58040)].
scientific article; zbMATH DE number 2102582