摘要
利用临界点理论中的极大极小作用原理获得了非自治二阶哈密顿系统ü=F(t,u(t)),a.e.t∈[0,T]u(0)-u(T)=.u(0)-.u(T)=0周期解的存在性结果.其中T>0,F:[0,T]×RNR满足:对每个x∈RN,F(t,x)关于t是可测的;对几乎处处的t∈[0,T],F(t,x)关于x是连续可微的;存在a∈C(R+,R+)和b∈L1(0,T;R+)使得|F(t,x)|≤a(|x|)b(t)|F(t,x)|≤a(|x|)b(t)对所有的x∈RN和几乎处处的t∈[0,T]都成立.
The existence of periodic solutions is obtained for nonautonomous second order Hamiltonian systems=▽F（t,u（t））,a.e.t∈[0,T]u（0）-u（T）=（0）-（T）=0where T0,and F：[0,T]×R^N→R satisfies assumption：which says that F（t,x）is measurable in t for every x∈RN and continuously differentiable in x for a.e.t∈[0,T],and there exist a∈C（R^＋,R^＋）,b∈L1（0,T;R^＋）such that｜F（t,x）｜≤a（｜x｜）b（t）｜▽F（t,x）｜≤a（｜x｜）b（t）for all x∈R^N and a.e.t∈[0,T].The existence of solutions is proved by the minimax method in critical point theory.
出处
《西南大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第4期110-114,共5页
Journal of Southwest University(Natural Science Edition)
基金
国家自然科学基金资助项目(10771173)
