论文标题
渐近恒定差分运算符和应用的光谱的扰动
Perturbation of the spectra for asymptotically constant differential operators and applications
论文作者
论文摘要
我们研究了具有渐近恒定系数的一类差分运算符的光谱。这些操作员广泛出现，因为非线性偏微分方程对模式或非线性波的线性化。我们提出了一个统一的框架，以证明相关光谱上的扰动结果。该证明基于指数二分法和布鲁维尔学位理论。作为应用，我们采用了开发的理论来研究金茨堡 - 兰道方程的准周期溶液的稳定性，反应扩散系统的折叠式分叉周期性解决方案与普通微分方程以及多皮子汉堡汉堡式汉堡模型的周期性环相结合。
We study the spectra for a class of differential operators with asymptotically constant coefficients.These operators widely arise as the linearizations of nonlinear partial differential equations about patterns or nonlinear waves. We present a unified framework to prove the perturbation results on the related spectra. The proof is based on exponential dichotomies and the Brouwer degree theory. As applications, we employ the developed theory to study the stability of quasi-periodic solutions of the Ginzburg-Landau equation,fold-Hopf bifurcating periodic solutions of reaction-diffusion systems coupled with ordinary differential equations, and periodic annulus of the hyperbolic Burgers-Fisher model.
