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

Wenxian Shen; Xiaoxia Xie

doi:10.3934/dcdsb.2017051

Article Contents

2017, Volume 22, Issue 3: 1023-1047. Doi: 10.3934/dcdsb.2017051

This issue Previous Article Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer Next Article Advection control in parabolic PDE systems for competitive populations

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

Wenxian Shen^1, , and
Xiaoxia Xie^2,

1.
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
2.
Department of Mathematics and Statistisc, Idaho State University, Pocatello, ID 83209, USA

Author Bio: E-mail address: wenxish@auburn.edu; E-mail address: xiexia2@isu.edu
* Corresponding author: Wenxian Shen
* Corresponding author: Wenxian Shen

Dedicate to Professor Stephen Cantrell on the occasion of his 60th birthday

Received: November 2015

Revised: July 2016

Published: September 2017

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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.

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

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