一类满足非Ambrosetti-Rabinowitz型超二次条件的受迫二阶Hamilton系统次调和解

Subharmonic Solutions of a Class of Forced Second-order Hamiltonian Systems With Non-Ambrosetti and Rabinowitz Type Superquadratic Condition

考虑一类受迫的二阶Hamilton系统,其中■-Kq(t,q)+Wq(t,q)=f(t),其中K,W和f关于变量t都是T-周期的,K满足b1|q|2≤K(t,q)≤b2|q|2,W满足非Ambrosetti-Rabinowitz型超二次条件(▽W(t,q),q)-2W(t,q)≥d2|q|μ-β(t).对每个k∈N,利用山路引理的一个变形,可以证明上述系统存在非平凡的2kT-周期解(即次调和解).

In this paper, a class of forced second order Hamiltonian systems = f（t） is discussed, where K, W∈C^1 （R＊R^n ,R）, and f∈ L^2 （R,R^n） are T-periodic in t,K（t,q） satisfies the pinching condition b1│q│^2≤K（t,q）≤b2│q│^2, and Rabinowitz type superquadratic condition （ △W（t,q）,q）-2W（t,q）≥d2│q│^-β（t） . The subharmonic solutions of the system can be obtained by using Mountain Pass Lemma.