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Positive solutions of impulsive boundary value problems for first-order nonlinear functional differential equations

机译:一阶非线性泛函微分方程的脉冲边值问题的正解

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摘要

In this paper, we study the problem on the existence of positive solutions for a class of impulsive periodic boundary value problems of first-order nonlinear functional differential equations. By using the fixed point theorem in cones and some analysis techniques, we present some sufficient conditions which guarantee the existence of one and multiple positive solutions for the impulsive periodic boundary value problems. Our results generalize and improve some previous results. Moreover, our results show that positive solutions for the impulsive periodic boundary value problems may be yielded completely by some proper impulsive conditions (see Example 4.1 and Remark 4.2 in Sect. 4), and also implies that proper impulsive conditions are of great significance to simulate processes, optimal control, population model and so on.
机译:本文研究了一阶非线性泛函微分方程的脉冲周期边值问题的正解问题。通过使用圆锥中的不动点定理和一些分析技术,我们给出了一些充分的条件,这些条件保证了脉冲周期边值问题的一个和多个正解的存在。我们的结果可以概括和改进以前的结果。此外,我们的结果表明,某些适当的脉冲条件可能完全产生了脉冲周期边值问题的正解(请参见第4节中的示例4.1和备注4.2),这也意味着适当的脉冲条件对于仿真具有重要意义。流程,最佳控制,总体模型等。

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