二阶哈密尔顿系统的对称扰动(英文)  

Perturbations from Symmetric Second Order Hamiltonian Systems

作　　者：何万生[1] 裴瑞昌[1] 

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《应用数学》2014年第3期476-482,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(10671156)

摘　　要：我们研究二阶Hamiltonian系统-ü=▽F1(t,u)+ε▽F2(t,u)a.e.t∈[0,T]的多重周期解,其中ε是一个参数,T>0.F1(F2)∶R×RN→R关于t是T周期的,▽F1(t,x)关于x是奇的;并且Fi(t,x)(i=1,2)对所有x∈RN关于t是可测的,对几乎所有t∈[0,T]关于x是连续可微的,而且存在a∈C(R+,R+),b∈L+(0,T;R+)使得|Fi(t,x)|≤a(|x|)b(t),|▽Fi(t,x)|≤a(|x|)b(t)对所有x∈RN及几乎所有t∈[0,T]成立.我们对F1施加适当的条件,能够证明对任意的j∈N存在εj>0使得|ε|≤εj,则上述问题至少有j个不同的周期解.We study the multiplicity of periodic solutions for second order hamiltonian systems-ü=▽F1（t,u）＋ε▽F2（t,u）a.e.t∈[0,T],whereεis a parameter and T〉0,F1（F2）∶R×RN→Ris Tperiodic int,▽F1（t,x）is odd with respect to x,Fi（t,x）（i=1,2）is measurable intfor all x∈RNand continuously differentiable in xfor a.e.t∈ [0,T],and there exist a∈C（R＋,R＋）,b∈L＋（0,T;R＋）such that｜Fi（t,x）｜≤a（｜x｜）b（t）,｜▽Fi（t,x）｜≤a（｜x｜）b（t）for all x∈RNand a.e.t∈ [0,T].Under suitable conditions only on F1,we prove that for any j∈Nthere existsεj 〉0such that if｜ε｜≤εj,then the above problem possesses at least jdistinct periodic solutions.

关 键 词：扰动 对称 哈密尔顿系统 多重周期解 

分 类 号：O175.2[理学—数学]