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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions and applications

Pages: 1023 - 1047, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017051

 
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Wenxian Shen - Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849, United States (email)
Xiaoxia Xie - Department of Mathematics and Statistisc, Idaho State University, Pocatello, ID 83209, United States (email)

Abstract: In this paper, we study the spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions subject to Dirichlet type, Neumann type and spatial periodic type boundary conditions. We first obtain necessary and sufficient conditions for the existence of a unique positive principal spectrum point for such operators. We then investigate upper bounds of principal spectrum points and sufficient conditions for the principal spectrum points to be principal eigenvalues. Finally we discuss the applications to nonlinear mathematical models from biology.

Keywords:  Nonlocal dispersal operator, time periodic weight function, principal spectrum point, principal eigenvalue, KPP equations.
Mathematics Subject Classification:  45C05, 45M05, 45M20, 47G10, 92D25.

Received: November 2015;      Revised: July 2016;      Available Online: January 2017.

 References