Long, Yiming; Xu, Xiangjin Periodic solutions for a class of nonautonomous Hamiltonian systems. (English) Zbl 0960.37028 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 41, No. 3-4, 455-463 (2000). The authors deal with the existence of periodic solutions for a Hamiltonian system \[ J\dot z- B(t)z= \nabla H(t,z), \quad z\in \mathbb{R}^{2N}, \quad t\in \mathbb{R}, \tag{1} \] where \(B(t)\) is a given \(T\)-periodic and symmetric \(2N\times 2N\) matrix function of class \(C^1\) in \(t\), \(H\in C^1 (\mathbb{R}\times \mathbb{R}^{2N}, \mathbb{R})\) is \(T\)-periodic in \(t\), \(\nabla H:= \nabla _z H\in C(\mathbb{R}\times \mathbb{R}^{2N}, \mathbb{R}^{2N})\) and \(J\) is the standard symplectic matrix. Under some natural conditions on \(H\), the authors prove the existence of \(T\)-periodic solutions of (1). Reviewer: Messoud Efendiev (Berlin) Cited in 13 Documents MSC: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 34C25 Periodic solutions to ordinary differential equations 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems Keywords:periodic solutions; Hamiltonian system; symplectic matrix PDFBibTeX XMLCite \textit{Y. Long} and \textit{X. Xu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 41, No. 3--4, 455--463 (2000; Zbl 0960.37028) Full Text: DOI