SUBHARMONIC SOLUTIONS AND MINIMAL PERIODIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

摘要

Maslov-type index; Morse index; homologically link; subharmonic solution; minimal period Using a homologically link theorem in variational theory and iteration inequalities of Maslov-type index, we show the existence of a sequence of subharmonic solutions of non-autonomous Hamiltonian systems with the Hamiltonian functions satisfying some anisotropic growth conditions, i.e., the Hamiltonian functions may have simultaneously, in different components, su-perquadratic, subquadratic and quadratic behaviors. Moreover, we also consider the minimal period problem of some autonomous Hamiltonian systems with anisotropic growth.