Subharmonic Solutions and Minimal Periodic Solutions of First-order Hamiltonian Systems with Anisotropic Growth

摘要

Using a homologically link theorem in variational theory and iterationinequalities of Maslov-type index, we show the existence of a sequence ofsubharmonic solutions of non-autonomous Hamiltonian systems with theHamiltonian functions satisfying some anisotropic growth conditions, i.e., theHamiltonian functions may have simultaneously, in different components,superquadratic, subquadratic and quadratic behaviors. Moreover, we alsoconsider the minimal period problem of some autonomous Hamiltonian systems withanisotropic growth.