一类带阻尼的吸引型奇性Duffing方程周期正解的存在性  

Positive Periodic Solutions for a Damped Duffing Equation with Singularity of Attractive Type

作　　者：夏晨阳 王振辉[1] 程志波[1] Chenyang Xia;Zhenhui Wang;Zhibo Cheng(School of Mathematics and Information Science,Henan Polytechnic University,Henan Jiaozuo 454003)

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454003

出　　处：《数学物理学报（A辑）》2022年第1期131-138,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11501170);河南省高校科技创新人才项目(2lHASTIT025)。

摘　　要：该文考虑了一类带阻尼的吸引型奇性Duffing方程u"(t)+Cu’(t)+g(u(t))=e(t),其中C是常数且C≠0,g是连续函数并且在原点x=0有吸引型奇性.通过应用Manasevich-Mawhin连续定理和一些分析方法,证明了该方程至少存在一个周期正解.In this paper,we consider a damped Duffing equation with singularity of attractive type u"(t)+Cu’(t)+g(u(t))=e(t),where C is a constant and C ≠0,g is a continuous function and has an attractive singularity at u= 0.By applications of Manasevich-Mawhin continuation theorem and some analysis skill,we establish some sufficient conditions for the existence of positive T-periodic solutions for this equation.

关 键 词：DUFFING方程 Manasevich-Mawhin定理 吸引型奇性 强弱奇性 周期正解 

分 类 号：O175.1[理学—数学]