没有(AR)条件的一类二阶Hamilton系统的同宿解

Homoclinic Solutions for A Class of the Second Order Hamiltonian System without(AR) Condition

利用标准版本的山路定理证明了二阶Hamilton系统:q+Vq(t,q)=f(t)在一些弱于(AR)条件的假设下,存在非平凡的同宿解.一个同宿轨道可以作为一序列二阶微分方程的2kT周期解的极限来得到.

In this paper, the existence of homoclinic solutions of the second order Hamihonian system . q ＋ Vq（t,q） =f（t） （HS） is considered using a standard version of the mountain pass theorem, some assumptions are given which is weaker than the （AR） condition. A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second order differential equations.