Joanna Janczewska

Gdansk University of Technology (Poland)

Homoclinic solutions for a class of Hamiltonian systems”

We study the existence of homoclinic orbits for the second order Hamiltonian system q+ V q(t,q) = f(t), where q ∈ Rn and V ∈ C1(R × Rn,R), V (t,q) = -K(t,q) + W(t,q) is T-periodic in t. A map K satisfies the ”pinching” condition b1|q|2 K(t,q) b2|q|2, W is superlinear at the infinity and f is sufficiently small in L2(R,Rn). A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second order differential equations.