共振条件下具有奇异性和无界扰动Duffing方程的周期解(下)

Periodic Solutions of Duffing Equations with Singularities and Unbounded Perturbations at Resonance

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.