论文标题
通过程度理论中关于连续微分方程中周期性解决方案存在的高级分析
Higher order analysis on the existence of periodic solutions in continuous differential equations via degree theory
论文作者
论文摘要
最近，根据Brouwer学位理论，开发了较高的较高平均方法，用于研究Lipschitz微分方程和不连续的分段平滑微分方程的周期性解决方案。在Lipschitz和不连续的分段平滑微分方程之间，对于周期性解决方案的存在，在更高级分析中缺乏一类巨大的微分方程，即连续的非lipschitz微分方程类别。在本文中，基于非线性操作员方程的一致性理论，我们对连续（非lipschitz）扰动微分方程进行更高级分析，并为这种系统的周期性解决方案提供了足够的条件。 We apply our results to study continuous (non-Lipschitz) higher order perturbations of a harmonic oscillator.
Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth differential equations was developed in terms of Brouwer degree theory. Between the Lipschitz and the discontinuous piecewise smooth differential equations, there is a huge class of differential equations lacking in a higher order analysis on the existence of periodic solutions, namely the class of continuous non-Lipschitz differential equations. In this paper, based on the coincidence degree theory for nonlinear operator equations, we perform a higher order analysis of continuous (non-Lipschitz) perturbed differential equations and derive sufficient conditions for the existence of periodic solutions for such systems. We apply our results to study continuous (non-Lipschitz) higher order perturbations of a harmonic oscillator.
