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Principal eigenvalues for some nonlocal eigenvalue problems and applications

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


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