Positive eigenfunctions for nonlocal dispersal problems

Abstract In this paper, we investigate the positive eigenfunctions for a class of weighted nonlocal eigenvalue problems. Using some nonlocal estimates and a nonlinear functional, we obtain the existence of a principal eigenvalue and its variational characterization.

[1]  J. López-Gómez.  Metasolutions of Parabolic Equations in Population Dynamics , 2015 .

[2]  Paul C. Fife,et al.  Some Nonclassical Trends in Parabolic and Parabolic-like Evolutions , 2003 .

[3]  J. Coville.  On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators , 2010, 1106.5137.

[4]  Yuan Lou,et al.  Random dispersal vs. non-local dispersal , 2009 .

[5]  Jerome Coville,et al.  Pulsating fronts for nonlocal dispersion and KPP nonlinearity , 2013, 1302.1053.

[6]  Song-Sun Lin,et al.  On the existence of positive eigenfunctions for an eigenvalue problem with indefinite weight function , 1980 .

[7]  Wenxian Shen,et al.  Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats , 2010 .

[8]  J. López-Gómez.  Linear Second Order Elliptic Operators , 2013 .

[9]  Peter W. Bates,et al.  Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal , 2007 .

[10]  J. López-Gómez.  The Maximum Principle and the Existence of Principal Eigenvalues for Some Linear Weighted Boundary Value Problems , 1996 .

[11]  Julio D. Rossi,et al.  A logistic equation with refuge and nonlocal diffusion , 2009 .

[12]  V. Volpert.  Nonlocal Reaction-diffusion Equations , 2014 .

[13]  E. Valdinoci,et al.  Liouville type results for a nonlocal obstacle problem , 2017, Proceedings of the London Mathematical Society.

[14]  Wan-Tong Li,et al.  Blow-up profiles for positive solutions of nonlocal dispersal equation , 2015, Appl. Math. Lett..

[15]  Noemi Wolanski,et al.  Boundary fluxes for nonlocal diffusion , 2007 .

[16]  Qihong Shi,et al.  Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit , 2019, Mathematical Methods in the Applied Sciences.

[17]  V. Hutson,et al.  The evolution of dispersal , 2003, Journal of mathematical biology.

[18]  Wan-Tong Li,et al.  A nonlocal dispersal equation arising from a selection-migration model in genetics , 2014 .

[19]  Wan-Tong Li,et al.  Asymptotic behavior for nonlocal dispersal equations , 2010 .

[20]  Louis Dupaigne,et al.  Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations , 2010, 1004.1906.

[21]  H. Berestycki,et al.  On the definition and the properties of the principal eigenvalue of some nonlocal operators , 2015, 1512.06529.

[22]  J. López-Gómez.  On the Structure and Stability of the Set of Solutions of a Nonlocal Problem Modeling Ohmic Heating , 1998 .