二阶非线性泛函微分方程的周期性解证明
On Certification of Periodic Solutions for Second-order Nonlinear Functional Differential Equations
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摘要: 二阶的非线性泛函微分方程，对于准确表达动力反馈系统具有重要意义。该文主要针对二阶非线性泛函微分方程解的性质展开研究。首先，给出了3个重要的概念：方程的振动、微分方程的周期性解、连续算子在有界开子集上是紧的。其次，对两种情况下的二阶非线性泛函微分方程解的振动性进行研究并给出相关结论。最后，对二阶非线性泛函微分方程解的周期性展开研究。这一研究由偏差变元Lienard方程开始，结合马林延拓定理，确定了其周期性解存在的4个条件，并给出了完整的证明过程。Abstract: Two order nonlinear functional differential equations ,for the accurate expression of the dynamic feedback system is of great significance .In this paper ,the properties of solutions have been studied for two order nonlinear functional differential equations .First of all ,three important concepts have been giv‐en:the periodic solutions of the equations ,the periodic solutions of the differential equations ,and the con‐tinuous operators on the bounded open subset .Second ,the oscillation of the solutions has been studied of the two order nonlinear functional differential equations and the relevant conclusions been given .Finally , the periodic expansion of the solutions of the two order nonlinear functional differential equations has also been studied .This study by the deviation variable element Lienard equation has begun with Marin continu‐ation theorem to determine the periodic solution existence of four conditions ,and gives the complete proof .
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