Nonlocal dispersal equations with almost periodic dependence. I. Principal spectral theory

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. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This series of two papers focuses on the study of principal spectral theory of nonlocal dispersal operators with almost periodic dependence and the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence. The first part investigates top Lyapunov exponents and generalized principal eigenvalues, providing various characterizations and studying the impact of time and space variations on them. The second part will apply the developed principal spectral theory to study the asymptotic dynamics of nonlinear nonlocal dispersal equations.