小阻尼时变双项位势Duffing型方程的调和解  

Research on Harmonic Solutions for the Duffing-Type Equations with Small Damping and Two-Term Time Dependent Potential

作　　者：魏亚男 Wei Ya’nan(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2023年第4期106-110,共5页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11971059)资助。

摘　　要：本文利用弯曲扭转拓扑映射的不动点定理,证明了如下结果:若a(t),b(t)是连续的T-周期函数,则小阻尼Duffing型方程x″+εx′+a(t)f(x)+b(t)g(x)=0至少存在四个调和解。In this article,by using fixed the point theorems for topological bend-twist maps,under relatively some natural conditions,we prove that for the small damping Duffing-type equation x″+εx′+a(t)f(x)+b(t)g(x)=0,there are at least four harmonic solutions starting from a starlike annulus on the phase plane.Here a(t) and b(t) are continuous T-periodic functions.

关 键 词：小阻尼 双项位势 DUFFING型方程 周期解 弯曲扭转定理 

分 类 号：O175.12[理学—数学]