This paper is to investigate the dependence of the principal spectrum pointsof nonlocal dispersal operators on underlying parameters and to consider itsapplications. In particular, we study the effects of the spatial inhomogeneity,the dispersal rate, and the dispersal distance on the existence of theprincipal eigenvalues, the magnitude of the principal spectrum points, and theasymptotic behavior of the principal spectrum points of nonlocal dispersaloperators with Dirichlet type, Neumann type, and periodic boundary conditionsin a unified way. We also discuss the applications of the principal spectraltheory of nonlocal dispersal operators to the asymptotic dynamics of twospecies competition systems with nonlocal dispersal.
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