In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations $$\begin{aligned} x''+\alpha x' +a(t)x^{n}-b(t)x^{n+1}+c(t)x^{n+2}=0, \end{aligned}$$ where $$\alpha \in {\mathbb {R}} $$ is a constant, n is a finite positive integer, and a(t), b(t), c(t) are continuous periodic functions. By using Mawhin’s continuation theorem, we prove the existence and multiplicity of positive periodic solutions for these equations.

中文翻译：

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一类二阶常微分方程周期解的存在性和多重性

本文研究一类非自治二阶常微分方程$$\begin{aligned} x''+\alpha x' +a(t)x^{n}的正周期解的存在性-b(t)x^{n+1}+c(t)x^{n+2}=0, \end{aligned}$$ where $$\alpha \in {\mathbb {R}} $$是常数，n是有限正整数，a(t)、b(t)、c(t)是连续周期函数。通过使用 Mawhin 连续定理，我们证明了这些方程的正周期解的存在性和多重性。