Advisor: Professor Martin Schechter
Abstract:

We consider the problem of proving the existence of periodic solutions for
a second order nonautonomous Hamiltonian system in n-dimensional Euclidean
space. We assume the dynamic behavior is determined by a nonautonomous
linear term and a nonautonomous gradient term which must be continuous and
linearly bounded. By proving the existence of a critical point for a
nonlinear functional acting on an appropriate function space we find
conditions for the existence of weak solutions when neither the linear nor
the nonlinear contribution to the dynamic behavior is dominant. We
consider the case where the dynamic behavior is determined only by the
nonautonomous gradient term. We also give conditions for the existence of
classical solutions.