Quasi-periodic solutions for differential equations with an elliptic equilibrium under delayed perturbation
Quasi-periodic solutions for differential equations with an elliptic equilibrium under delayed perturbation
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DOI：
10.1016/j.jde.2023.10.052
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发表时间：
2024-01
影响因子：
2.4
通讯作者：
Xiaolong He
中科院分区：
文献类型：
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作者：
Xiaolong He
利用Craig-Wayne-Bourgain（CWB）方法构造了一类非线性时滞扰动方程的拟周期解.在迭代的每一步中的线性化方程是环面上的微分-差分方程。我们将联合收割机中的绿色函数估计技术和KAM理论中的约简方法结合起来求解线性方程组，推广了CWB方法的适用性。作为应用，我们研究了一类具有拟周期系数和时滞的Lotka-Volterra方程的正拟周期解.
We employ the Craig-Wayne-Bourgain (CWB) method to construct quasi-periodic solutions for the nonlinear delayed perturbation equations. The linearized equation at each step of the iterations is a differential-difference equation on the torus. We shall combine the techniques of Green's function estimate and the reducibility method in KAM theory to solve the linear equation, which generalizes the applicability of the CWB method. As an application, we study the positive quasi-periodic solutions for a class of Lotka-Volterra equations with quasi-periodic coefficients and time delay.