弱连续映射的拓扑度理论及其应用(英文)  

Topological Degree Theory for Weakly Continuous Mappings and Its Applications

作　　者：唐春雷[1] 刘玲[2] 从志坚 

机构地区：[1]西南师范大学数学系,重庆400715 [2]重庆交通学院职业技术学院,重庆400042 [3]楚雄师范高等专科学校中师部,云南楚雄675000

出　　处：《西南师范大学学报（自然科学版）》2002年第4期459-464,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金 (198710 67) ;教育部科学技术重点项目;高等学校优秀青年教师教学科研奖励计划

摘　　要：用有限维逼近方法建立了从可分自反Banach空间到其对偶空间的弱连续映射的拓扑度理论 .作为应用 。The topological degree theory is set up for weakly continuous mappings from a separable and reflexive Banach space into its dual space by using the idea of the fintis dimensional approximation. As an application we prove that the forced simple pendulum equation has at least two geometrically distinct periodic solutions when the L 1 norm of the forced term is sufficiently small.

关 键 词：弱连续映射 拓扑度理论 受迫单摆方程 周期解 可分自反Banach空间 有限维逼近方法 

分 类 号：O177.91[理学—数学]