New existence of periodic solutions for second order non-autonomous Hamiltonian systems
The authors consider the second order Hamiltonian system \(\ddot x(t)-B(t)x(t)+\nabla H(t,x)=0\). They show that under some conditions on \(B\) and \(H\) this system has a nontrivial periodic solution. The results extend those contained in [\textit{X. M. He} and \textit{X. Wu}, J. Math. Anal. Appl. 341, No. 2, 1354--1364 (2008; Zbl 1133.37025)]. The proofs use a linking and a local linking argument for the Euler-Lagrange functional corresponding to the problem.
scientific article; zbMATH DE number 5731692
scientific article