非自治Hamilton系统多重次调和最小周期解(英文)

Multiple Subharmonic Solutions of Nonautonomous Hamiltonian System

中文摘要:

      本文利用了z_p-指标和伪指标研究了非自治超二次Hamilton系统Jz=H_z(z(t),t),z(0)=z(2πp)次调和多重最小周期解,其中H(z,t+2πp)=H(z,t),t∈R^N,z∈R^2N.在假设H₁-H₄条件下,系统至少存在kN个不同的以2πp为最小周期的解.

英文摘要:

      By means of Z_p-index and its pseudo-index, we study the existence of multiple subharmonic solutions with prescribed minimal period for nonautonomous su-perquadratic Hamiltonian system Jz = H_z(z(t),t),z(0) = z(2πp) where H(z, t + 2πp) = H(z, t), t ∈ R, z∈R^2N. Under hypotheses H1-H4, there are at least kN distinct soultions with minimal period 2-πp.