The existence and multiplicity of T-periodic solutions to a class of differential equations with attractive singularities at the origin are investigated in the paper. The approach is based on a new method of construction of strict upper and lower functions. The multiplicity results of Ambrosetti–Prodi type are established using a priori estimates and certain properties of topological degree.

中文翻译：

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具有吸引奇点的微分方程的周期解的存在性和多重性

研究了一类原点具有吸引奇点的微分方程的T-周期解的存在性和多重性。该方法基于一种构造严格上下函数的新方法。Ambrosetti-Prodi 类型的多重性结果是使用先验估计和拓扑度的某些属性建立的。