摘要
本文考虑Lagrange系统 d/dt ?/?(q,q)-?/?q(q,q)=0 (?)这儿?(q,ξ)=1/2 wum form i,j=1 to n a_(ij)(q)eξξ-V(q),q∈R^n,ξ∈R^n 。假设位势函数V有界,并且lim V(q)/|q|~2 =δ>0,V(q)=V(-q),则系统(?)具有一个以适当大的正数T为周期的非平凡解。
The following Lagrangian system is consideredd/dt ??/?ξ(q,q)-??/?q(q,q)=0 (?)where ?(q,ξ)=1/2 sub from i,j=1 to n α_(ij)(q)ξ_iξ_j-V(q),(q,ξ)∈R^n×R^n. Under the assumption of abounded potential Ⅴ and lim q→0 V(q)/|q|~2=δ>0, V(q)=V(-q)(?) admits a periodic solution with minimal period T, for any T>2π(r/δ)^(1/2), where r isthe largest eigenvalue of {au(0)}.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1996年第2期159-166,共8页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
