Variational Approach to Quasi-Periodic Solution of Nonautonomous Second-Order Hamiltonian Systems

Periodic Solutions of Second Order Hamiltonian Systems

We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′ x (t, x) , where ε is a small parameter, x ∈ R and V (t, x) is 2π-periodic in t. Moreover we provide two applications.

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.

On periodic solutions of nonautonomous second order Hamiltonian systems with ( q , p ) - Laplacian

A new existence result is obtained for nonautonomous second order Hamiltonian systems with (q, p)-Laplacian by using the minimax methods.

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

Periodic Solutions of Second-order Nonautonomous Dynamical Systems