Abstract We give a lower estimate of the number of anti-periodic solutions of implicit differential inclusions on tori. Our approach is based on the application of the topological essential fixed point theory, jointly with the Nielsen theory for multivalued admissible maps. Since one of the conditions is rather technical (zero topological dimension of a fixed point set), some simple illustrative examples to the main theorem are supplied. In the single-valued case of implicit differential equations, relevant arguments are still discussed in concluding remarks.

中文翻译：

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环上隐微分包含的多重反周期解

摘要 我们对环上隐微分包含的反周期解的数量给出了一个较低的估计。我们的方法基于拓扑基本不动点理论的应用，以及多值可容许地图的尼尔森理论。由于其中一个条件相当技术性（不动点集的拓扑维数为零），因此提供了一些主要定理的简单说明性示例。在隐式微分方程的单值情况下，相关论点仍在结束语中讨论。