论文标题
具有几乎周期性依赖性的非局部分散方程。 I.主要光谱理论
Nonlocal dispersal equations with almost periodic dependence. I. Principal spectral theory
论文作者
论文摘要
这两篇论文专门研究具有几乎周期性依赖性的非局部分散操作员的主要光谱理论，并研究了非线性非局部分散方程的渐近动力学，并且几乎是周期性的。在该系列的第一部分中，我们研究了两个方面的非局部分散操作员的主要光谱理论：顶级Lyapunov指数和广义的主要特征值。除其他外，我们还提供了顶级Lyapunov指数和广义的主要特征值的各种特征，建立它们之间的关系，并研究时间和空间变化对它们的影响。在该系列的第二部分中，我们将研究非线性非局部分散方程的渐近动力学，几乎是周期性依赖性的，并应用了本部分中要开发的主要光谱理论。
This series of two papers is devoted to the study of the principal spectral theory of nonlocal dispersal operators with almost periodic dependence and the study of the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence. In this first part of the series, we investigate the principal spectral theory of nonlocal dispersal operators from two aspects: top Lyapunov exponents and generalized principal eigenvalues. Among others, we provide various characterizations of the top Lyapunov exponents and generalized principal eigenvalues, establish the relations between them, and study the effect of time and space variations on them. In the second part of the series, we will study the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence applying the principal spectral theory to be developed in this part.
