非局部扩散方程主Eigenvalue存在的充分条件及其应用
A Sufficient Condition for the Existence of a Principal Eigenvalue for Nonlocal Diffusion Equations with Applications
摘要：
对于非局部扩散方程的性质研究已经做了大量的工作。主本征值的存在一直是这项工作的重要组成部分。虽然有界区域上的主特征值方程的存在性有很好的结果，但无界区域上的结果很少。在有界域上，巴拿赫空间上的Krein-Rutman定理是证明存在性的常用工具。本文证明了推广的Krein-Rutman方法可用于无界区域，正算子理论可作为分析非局部扩散方程的有力工具.特别地，给出了主特征值存在的一个有用的充分条件。
英文摘要：
Considerable work has gone into studying the properties of nonlocal diffusion equations. The existence of a principal eigenvalue has been a significant portion of this work. While there are good results for the existence of a principal eigenvalue equations on a bounded domain, few results exist for unbounded domains. On bounded domains, the Krein-Rutman theorem on Banach spaces is a common tool for showing existence. This article shows that generalized Krein-Rutman can be used on unbounded domains and that the theory of positive operators can serve as a powerful tool in the analysis of nonlocal diffusion equations. In particular, a useful sufficient condition for the existence of a principal eigenvalue is given.
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