American Institute of Mathematical Sciences

July  2016, 36(7): 4027-4049. doi: 10.3934/dcds.2016.36.4027

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, China, China

Received  April 2015 Revised  November 2015 Published  March 2016

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.
Citation: Fei-Ying Yang, Wan-Tong Li, Jian-Wen Sun. Principal eigenvalues for some nonlocal eigenvalue problems and applications. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 4027-4049. doi: 10.3934/dcds.2016.36.4027
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