共振条件下具有奇异性和无界扰动Duffing方程的周期解(上)  

Periodic Solutions of Duffing Equations with Singularities and Unbounded Perturbations at Resonance

作　　者：马田田[1] 张铁荟[2] 黄艳[3] 

机构地区：[1]首都师范大学,北京100048 [2]济宁学院初等教育学院,山东曲阜273165 [3]枣庄职业学院基础教学部,山东枣庄277800

出　　处：《首都师范大学学报（自然科学版）》2017年第6期1-4,共4页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金青年基金(项目号:11501381)资助项目

摘　　要：本文研究了共振条件下具有奇异性和无界扰动Duffing方程周期解的存在性.应用相平面分析的方法和连续性定理证明了给定方程至少存在一个周期解.In this paper,we study the existence of periodic solutions of Duffing equations with singularities x″ ＋1/4n2x ＋g（ x） = p（ t）,（ n ∈ N）,where n is a positive integer and g：（ 0,＋ ∞） → R is locally Lipschitz continuous and has a singularity at the origin. By using phase plane analysis method and the continuation theorem,we prove that the given equation has at least one periodic solution provided that g is unbounded and satisfies sub-quadratic condition at infinity.

关 键 词：DUFFING方程 周期解 奇异性 连续性定理 

分 类 号：O175.1[理学—数学]