一类二阶非线性系统解的渐近性态  

Asymptotic of solutions to a class of nonlinear second-order systems

作　　者：李全国[1] 

机构地区：[1]暨南大学数学系,广东广州510632

出　　处：《暨南大学学报（自然科学与医学版）》2007年第3期221-223,共3页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金资助(60474048)

摘　　要：在齐次边界条件下,用无穷维动力系统的方法研究了一类二阶非线性系统的长时间行为.证明了当η+|β|<l_1^(1/2)ε′〔ε′=min〔α/4,l1/2α,(l1/2)^(1/2)〕〕时,该系统的平衡点是全局指数型吸引子,并将所得结果应用到系统能稳性的研究中.The long time behaviour of solutions of some nonlinear second-order systems is studied by the infinite dimensional dynamical system method, under nonhomomgeneous boundary conditions. The global attractor of the system is a equilibrium point when η＋｜β｜〈√γ1ε＇（ε＇=min（α/4,γ1/2α,√γ1/2））and it is exponentially attractive. Then asymptotic stability of the system is also proved. The result is applied to the study of the stabilizability of the control system.

关 键 词：二阶非线性系统 平衡点 全局吸引子 变分法 

分 类 号：O19[理学—数学]