On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators

65Citations
Citations of this article
13Readers
Mendeley users who have this article in their library.

Abstract

In this paper we are interested in the existence of a principal eigenfunction of a nonlocal operator which appears in the description of various phenomena ranging from population dynamics to micro-magnetism. More precisely, we study the following eigenvalue problem: ∫ωJ(x-y/g(y))φ(y)gn(y)/dy+a(x)φ=ρφ, where ω⊂R{double-struck}n is an open connected set, J a non-negative kernel and g a positive function. First, we establish a criterion for the existence of a principal eigenpair (λp,φp). We also explore the relation between the sign of the largest element of the spectrum with a strong maximum property satisfied by the operator. As an application of these results we construct and characterise the solutions of some nonlinear nonlocal reaction diffusion equations. © 2010.

Cite

CITATION STYLE

APA

Coville, J. (2010). On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators. Journal of Differential Equations, 249(11), 2921–2953. https://doi.org/10.1016/j.jde.2010.07.003

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free