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 + V _{q}(t,q) = f(t), where
q R^{n} and V C^{1}(R × R^{n},R), V (t,q) = K(t,q) + W(t,q) is Tperiodic in t. A map K satisfies the
”pinching” condition b_{1}q^{2} ≤ K(t,q) ≤ b_{2}q^{2}, W is superlinear at the infinity and f is sufficiently small in
L^{2}(R,R^{n}). A homoclinic orbit is obtained as a limit of 2kTperiodic solutions of a certain sequence of the
second order differential equations.
