This paper is mainly concerned with the generalised principal eigenvalue for time-periodic nonlocal dispersal operators. We first establish the equivalence between two different characterisations of the generalised principal eigenvalue. We further investigate the dependence of the generalised principal eigenvalue on the frequency, the dispersal rate and the dispersal spread. Finally, these qualitative results for time-periodic linear operators are applied to time-periodic nonlinear KPP equations with nonlocal dispersal, focusing on the effects of the frequency, the dispersal rate and the dispersal spread on the existence and stability of positive time-periodic solutions to nonlinear equations.

中文翻译：

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时间周期非局部扩散算子的广义主特征值及其应用

本文主要关注时间周期非局部扩散算子的广义主特征值。我们首先建立广义主特征值的两个不同特征之间的等价性。我们进一步研究了广义主特征值对频率、扩散率和扩散扩散的依赖性。最后，将这些时间周期线性算子的定性结果应用于具有非局部扩散的时间周期非线性 KPP 方程，重点研究频率、扩散率和扩散扩散对时间周期正解的存在性和稳定性的影响到非线性方程。