关于次二次哈密顿系统次调和解的研究(英文)  

The Study of Subharmonic Solutions for Subquadratic Hamiltonian Systems

作　　者：李翀[1] 

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《南开大学学报（自然科学版）》2014年第4期59-66,共8页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Partially supported by the National Natural Science Foundation of China(11226156);the “New Start” Academic Research Projects of Beijing Union University(ZK201218,ZK10201304)

摘　　要：运用Galerkin逼近的方法和Maslov型指标理论的迭代不等式研究了哈密顿系统z(t)=J▽H(t,z(t))次调和解的存在性,其中H(t,z)=1/2(B(t)z,z)+H(t,z),B(t)是半正定对称连续矩阵,H是非凸的、无界的和非一致强制的.同时还证明了这些解在一定的条件下是几何相异的.By the Galerkin approximation method and the iteration inequalities of the Maslov-type index theory, the existence of subharmonic solutions for the Hamiltonian system z（t）=J▽H（t,z（t））is studied,where H（t,z）=1/2（B（t）z,z）＋H（t,z）,B（t）is a semipositive symmetric continuous matrix and H is notconvex, unbounded and not uniformly coercive. There also obtains that these solutions are pairwise geometrical- ly distinct under the certain conditions.

关 键 词：Maslov型指标 次调和解 次二次Hamilton系统 

分 类 号：O175[理学—数学]