ISSN:
1432-1297
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Clarke has shown that the problem of findingT-periodic solutions for a convex Hamiltonian system is equivalent to the problem of finding critical points to a certain functional, dual to the classical action functional. In this paper, we relate the Morse index of the critical point to the minimal period of the correspondingT-periodic solution. In particular, we show that if the critical point is obtained by the Ambrosetti-Rabinowitz mountain-pass theorem the corresponding solution has minimal periodT, that is, it cannot beT/k-periodic withk integer,k≧2. As a consequence, we prove that if the Hamiltonian is flat near an equilibrium and superquadratic near infinity, then for anyT〉0, the corresponding Hamiltonian system has a periodic solution with minimal periodT.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01388776
