一类非自治三阶常微分方程周期解的存在性

Existence of periodic solutions for a class of nonautonomous third-order ordinary differential equations

摘要:

本文研究了一类非自治三阶常微分方程正周期解的存在性,其中$a(t),b(t),c(t)$是连续的$T-$周期函数.运用Mawhin延拓定理,本文证明了方程至少存在两个正的$T-$周期解.

Abstract:

In this paper, we study the existence of positive periodic solutions of a class of nonautonomous third-order ordinary differential equations where $a(t),b(t),c(t)$ are continuous T-periodic functions. By using the Mawhin's continuation theorem, we prove the existence of at least two positive T-periodic solutions for this equation.