Infinitely many periodic solutions for asymptotically linear Hamiltonian systems

Infinitely Many Periodic Solutions for Nonautonomous Sublinear Second-Order Hamiltonian Systems

and Applied Analysis 3 Our main result is the following theorem. Theorem 1.1. Suppose that F t, x satisfies assumptions (A) and 1.7 . Assume that lim sup r→ ∞ inf x∈RN,|x| r |x|−2α ∫T 0 F t, x dt ∞, 1.8 lim inf R→ ∞ sup x∈RN,|x| R |x|−2α ∫T 0 F t, x dt −∞. 1.9

Existence of Infinitely Many Periodic Solutions for Second-order Nonautonomous Hamiltonian Systems

By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.

Infinitely Many Periodic Solutions for Variable Exponent Systems

Infinitely Many Periodic Solutions to a Class of Perturbed Second–order Impulsive Hamiltonian Systems

We investigate the existence of infinitely many periodic solutions to a class of perturbed second-order impulsive Hamiltonian systems. Our approach is based on variational methods and critical point theory. Mathematics subject classification (2010): 34B15, 47J10.

Poincaré-birkhoff Fixed Point Theorem and Periodic Solutions of Asymptotically Linear Planar Hamiltonian Systems

This work, which has a self contained expository character, is devoted to the Poincaré-Birkhoff (PB) theorem and to its applications to the search of periodic solutions of nonautonomous periodic planar Hamiltonian systems. After some historical remarks, we recall the classical proof of the PB theorem as exposed by Brown and Neumann. Then, a variant of the PB theorem is considered, which enables...