Galerkin�s method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy

Crispin, D. J.; Toland, J. F.
June 2005
Calculus of Variations & Partial Differential Equations;Jun2005, Vol. 23 Issue 2, p205
Academic Journal
A combination of Galerkin�s method and linking theory with monotonicity in the calculus of variations is used to study Hamiltonian systems in which the kinetic-energy functional is a (not necessarily definite) quadratic form and the potential-energy functional may be bounded. The existence of non-constant brake periodic orbits for almost all prescribed energies is established. An example of a Hamiltonian system which satisfies our hypotheses but has no non-constant brake periodic orbits with energy in an uncountable set of measure zero is given. Additional hypotheses, sufficient to ensure the existence of non-constant brake periodic orbits of all energies, are found.


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