论文标题
非自我支持的雅各比操作员及其应用的几乎周期性的基态
Almost-periodic ground state of the non-self-adjoint Jacobi operator and its applications
论文作者
论文摘要
我们使用动力学系统的方法研究了几乎周期性介质中一维非自我配合的雅各比操作员的基态。我们展示了基态的存在。特别是，在准周期介质中，我们表明系数的规律性较低可以保证基础状态的存在。除此之外，我们提供了两个应用：第一个应用是显示离散Fisher-KPP类型方程的正稳态的存在和独特性；第二个应用是研究具有较大较低级项的离散固定抛物线方程的渐近行为。
We study the ground states of the one-dimensional non-self-adjoint Jacobi operators in the almost periodic media by using the method of dynamical systems. We show the existence of the ground state. Particularly, in the quasi-periodic media, we show that the lower regularity of coefficients can guarantee the existence of ground states. Besides that, we give two applications: the first application is to show the existence and uniqueness of the positive steady state of the discrete Fisher-KPP type equation; the second application is to investigate the asymptotic behavior of the discrete stationary parabolic equation with large lower order terms.
