Infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities

Boundary value problems

Yinyin Wu¹  Dingbian Qian² 

[1] Department of Fundamental Courses, Wuxi Institute of Technology, Wuxi, China;School of Mathematical Sciences, Soochow University, Suzhou, China

关键词: infinity of subharmonics;    convex and oscillatory nonlinearity;    time map;    Poincaré-Birkhoff twist theorem;   

DOI  :  10.1186/s13661-016-0729-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The existence of infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities is shown. This result is a corollary of two theorems. These theorems, one for a weak sub-quadratic potential and another for a geometric case, roughly speaking, are complementary. The approach of this paper is based on the phase-plane analysis for the time map and using the Poincaré-Birkhoff twist theorem.

【 授权许可】

CC BY