一类具有状态依赖偏差变元的一阶微分方程最小解和最大解的存在性
Existence of minimal and maximal solutions to first--order differential equations with state--dependent deviated arguments
摘要：
本文证明了一阶具偏差变元的常微分方程解的存在性的一些新结果。延迟微分方程包括在我们的一般框架，它甚至允许偏差依赖于未知的解决方案。我们的存在性结果依赖于本文引入的上下解的新定义，并通过一个例子证明了与经典定义类似的结果是错误的。我们还介绍了一个例子表明，所考虑的问题不需要有最小（或最大）的解决方案之间的上下解，但我们可以证明，他们确实有最小和最大的解决方案，在通常的集理论意义上。给出了上下解存在的充分条件，并给出了应用实例。
英文摘要：
We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the unknown solutions. Our existence results lean on new definitions of lower and upper solutions introduced in this paper, and we show with an example that similar results with the classical definitions are false. We also introduce an example showing that the problems considered need not have the least (or the greatest) solution between given lower and upper solutions, but we can prove that they do have minimal and maximal solutions in the usual set--theoretic sense. Sufficient conditions for the existence of lower and upper solutions, with some examples of application, are provided too.
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