Homoclinic solutions for second-order Hamiltonian systems with periodic potential

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.

Homoclinic solutions for a class of non-periodic second order Hamiltonian systems

We study the existence of homoclinic solutions for the second order Hamiltonian system ü+Vu(t, u) = f(t). Let V (t, u) = −K(t, u)+W (t, u) ∈ C1(R×Rn,R) be T -periodic in t, where K is a quadratic growth function and W may be asymptotically quadratic or super-quadratic at infinity. One homoclinic solution is obtained as a limit of solutions of a sequence of periodic second order differential equ...

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

Multiple Periodic Solutions for Perturbed Second-order Impulsive Hamiltonian Systems

The existence of three distinct periodic solutions for a class of perturbed impulsive Hamiltonian systems is established. The techniques used in the proofs are based on variational methods. AMS Subject Classification: 34B15

Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems

Some multiplicity results are obtained for periodic solutions of the nonautonomous superquadratic second-order discrete Hamiltonian systems Duðt 1Þ þ rF ðt; uðtÞÞ 1⁄4 0 8t 2 Z 0096-3 doi:10. q Sup Outsta * Co E-m Plea Com by using critical point theory, especially, a three critical points theorem proposed by Brezis and Nirenberg. 2007 Elsevier Inc. All rights reserved.