|
During the past thirty years there has been a great deal of progress
in the use of variational methods to find homoclinic and heteroclinic
solutions of Hamiltonian systems including Newtonian ones.
Such solutions are global in time. Therefore it is reasonable
to use global methods to receive them rather than by means of approaches
based on initial value problems. Moreover, solutions of Hamiltonian
systems are critical points of so called action functionals in suitable
functional spaces.
The study of quantity and quality of solutions of Hamiltonian systems
is a problem of great importance, since most of them derives for instance
from mechanics, theoretical physics and differential geometry.
We will discuss Hamiltonian systems under various assumptions on
a potential. We will show how to receive homoclinic and heteroclinic
solutions applying the approximative scheme developed by Janczewska,
Lion's concentration-compactness principle, Ekeland's principle,
minimax methods and the shadowing chain lemma for singular systems
by Izydorek and Janczewska.
|
