共振条件下具有无界扰动方程的周期解  

Periodic solutions of unbounded perturbation equations under resonance conditions

作　　者：邢秀梅 王志国[2] 黄强联[3] XING Xiumei;WANG Zhiguo;HUANG Qianglian(Institute of Applied Mathematics,Yili Normal University,Yining 835000,China;School of Mathematical Sciences,Soochow University,Suzhou 215006,China;School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]伊犁师范大学应用数学研究所,新疆伊宁835000 [2]苏州大学数学科学学院,江苏苏州215006 [3]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2022年第4期16-18,72,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(12071232,12071410,11771378);新疆自然科学基金资助项目(2019D01C336)。

摘　　要：考虑共振条件下一类具有无界扰动Duffing方程周期解的存在性,通过相平面分析方法和Poincaré-Bohn定理,证明了这类方程至少存在一个周期解.The existence of periodic solutions of Duffing equations at resonance is studied.By using phase plane analysis method and Poincaré-Bohn theorem,it is proved that the given equation has at least one periodic solution provided that the perturbed term is unbounded and satisfies sub-quadratic condition at infinity.

关 键 词：周期解 Poincaré-Bohn定理 共振 无界扰动 DUFFING方程 

分 类 号：O175.13[理学—数学]