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

This series of two papers is devoted to the study principal spectral theory nonlocal dispersal operators with almost periodic dependence and asymptotic dynamics nonlinear equations dependence. In this first part series, we investigate from aspects: top Lyapunov exponents generalized eigenvalues. Among others, provide various characterizations eigenvalues, establish relations between them, effect time space variations on them. second will applying be developed in part.