一类具有偏差变元的Lienard型方程的周期解

Periodic Solutions of The Lienard-type Equation with Delays and Deviating Argument

关键词:  Lienard型方程  周期解  存在性  重合度

Key words:  Lienard-type equation  periodic solutions  existence  coincidence degree

摘要:

利用Mawhin重合度理论,研究一类具有偏差变元Lienard型方程x″(t)+∑_i=1ⁿh_i(x)|x'|^2α_i+f(t,x(t),x(t-τ₀)))x'(t)+g(t,x(t-τ₁(t)))=p(t)的周期解的存在性,得到其周期解存在的新的充分条件,推广和改进文献[1,2]的相关结果.

Abstract:

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions of the Lienard-type equation x″ (t)+∑_i=1ⁿh_i (x)|x'|^2α_i+f (t, x (t), x (t-τ₀)))x' (t)+g (t, x (t-τ₁ (t)))=p (t) with delays and deviating argument, Some new sufficient condition of periodic solutions is obtained. The results on reference[1, 2] are extended and improved.