Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems

SUBHARMONIC SOLUTIONS FOR NONAUTONOMOUS SUBLINEAR p–HAMILTONIAN SYSTEMS

Some existence theorems are obtained for subharmonic solutions of nonautonomous p -Hamiltonian systems by the minimax methods in critical point theory. Mathematics subject classification (2010): 34C25.

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

Subharmonic Solutions for First-order Hamiltonian Systems

In this article, we study the existence of periodic and subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems such that the nonlinearity has a growth at infinity faster than |x|α, 0 ≤ α < 1. We also study the minimality of periods for such solutions. Our results are illustrated by specific examples. The proofs are based on the least action principle and a generaliz...

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.

Subharmonic solutions and homoclinic orbits of second order discrete Hamiltonian systems with potential changing sign