Skip to Main content Skip to Navigation
Journal articles

Singular measure as principal eigenfunction of some nonlocal operators

Abstract : In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator. That is, we look for the existence of some particular solution (lambda, phi) of a nonlocal operator: integral(Omega) K(x, y)phi(y) dy + a(x)phi(x) = -lambda phi(x), where Omega subset of R-n is a bounded domain, K is a nonnegative kernel and a is continuous. We prove that for the generalised principal eigenvalue lambda(p) := sup{lambda is an element of R vertical bar there exists phi is an element of C(Omega), phi > 0 so that L-Omega[phi]+a(x)phi + lambda phi <= 0} there exists always a solution (d mu, lambda(p)) of the problem in the space of positive measure. When d mu, is absolutely continuous with respect to the Lebesgue measure, d(mu) = phi(p) (x)dx is called the principal eigenfunction associated with lambda(p),. In some simple cases, we exhibit some explicit singular measures that are solutions of the spectral problem.
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

https://hal.inrae.fr/hal-02646347
Contributor : Migration Prodinra <>
Submitted on : Friday, May 29, 2020 - 4:35:15 AM
Last modification on : Monday, November 30, 2020 - 6:42:01 PM

File

J.Coville POSTPRINT_1.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Jerome Coville. Singular measure as principal eigenfunction of some nonlocal operators. Applied Mathematics Letters, Elsevier, 2013, 26 (8), pp.831-835. ⟨10.1016/j.aml.2013.03.005⟩. ⟨hal-02646347⟩

Share

Metrics

Record views

24

Files downloads

82