We extend to delay equations recent results obtained by G. Feltrin and F. Zanolin for second-order ordinary equations with a superlinear term. We prove the existence of positive periodic solutions for nonlinear delay equations −u″(t) = a(t)g(u(t), u(t − τ)). We assume superlinear growth for g and sign alternance for a. The approach is topological and based on Mawhin’s coincidence degree. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

中文翻译：

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基于拓扑度的超线性时滞方程的周期正解

我们扩展到延迟方程最近由 G. Feltrin 和 F. Zanolin 获得的具有超线性项的二阶常方程的结果。我们证明了非线性延迟方程 -u″(t) = a(t)g(u(t), u(t − τ)) 的正周期解的存在。我们假设 g 的超线性增长和 a 的符号交替。该方法是拓扑的，并且基于 Mawhin 的重合度。本文是主题问题“微分和差分方程中的拓扑度和不动点理论”的一部分。