Principal eigenvalues for some nonlocal eigenvalue problems and applications

Fei-Ying  Yang; Wan-Tong Li; Jian-Wen Sun

doi:10.3934/dcds.2016.36.4027

Article Contents

2016, Volume 36, Issue 7: 4027-4049. Doi: 10.3934/dcds.2016.36.4027

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Principal eigenvalues for some nonlocal eigenvalue problems and applications

1.
School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000

Received: March 31, 2015

Revised: October 31, 2015

Published: May 2017

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Abstract

This paper is concerned with the principal eigenvalues of some nonlocal operators. We first derive a result on the limit of certain sequences of principal eigenvalues associated with some nonlocal eigenvalue problems. Then, such a result is used to study the existence, uniqueness and asymptotic behavior of positive solutions to a nonlocal stationary problem with a parameter. Finally, the long-time behavior of the solutions of the corresponding nonlocal evolution equation and the asymptotic behavior of positive stationary solutions on parameter are discussed.

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Mathematics Subject Classification: Primary: 35B40, 45A05; Secondary: 47G20.

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