On principal spectrum points/principal eigenvalues of nonlocal dispersaloperators and applications

Wenxian Shen; Xiaoxia Xie

doi:10.3934/dcds.2015.35.1665

Article Contents

2015, Volume 35, Issue 4: 1665-1696. Doi: 10.3934/dcds.2015.35.1665

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On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications

Wenxian Shen^1, and
Xiaoxia Xie^2,

1.
Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849
2.
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received: July 31, 2013

Revised: May 31, 2014

Published: May 2017

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Abstract

This paper is to investigate the dependence of the principal spectrum points of nonlocal dispersal operators on underlying parameters and to consider its applications. In particular, we study the effects of the spatial inhomogeneity, the dispersal rate, and the dispersal distance on the existence of the principal eigenvalues, the magnitude of the principal spectrum points, and the asymptotic behavior of the principal spectrum points of nonlocal dispersal operators with Dirichlet type, Neumann type, and periodic boundary conditions in a unified way. We also discuss the applications of the principal spectral theory of nonlocal dispersal operators to the asymptotic dynamics of two species competition systems with nonlocal dispersal operators.

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Mathematics Subject Classification: 45C05, 45M05, 45M20, 47G10, 92D25.

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