Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic 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.

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems