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所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″ +(1/4) n^2 x +g( x) = p( t),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.
出处
《首都师范大学学报(自然科学版)》
2018年第1期1-7,共7页
Journal of Capital Normal University:Natural Science Edition
基金
国家自然科学基金青年基金(11501381)资助项目
关键词
DUFFING方程
周期解
奇异性
连续性定理
Duffing equations, singularity, periodic solution, continuation theorem.