Spectral properties of non-local uniformly-elliptic operators

Date

2006-10-11

Authors

Davidson, Fordyce A.
Dodds, Niall

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

In this paper we consider the spectral properties of a class of non-local uniformly elliptic operators, which arise from the study of non-local uniformly elliptic partial differential equations. Such equations arise naturally in the study of a variety of physical and biological systems with examples ranging from Ohmic heating to population dynamics. The operators studied here are bounded perturbations of linear (local) differential operators, and the non-local perturbation is in the form of an integral term. We study the eigenvalues, the multiplicities of these eigenvalues, and the existence of corresponding positive eigenfunctions. It is shown here that the spectral properties of these non-local operators can differ considerably from those of their local counterpart. However, we show that under suitable hypotheses, there still exists a principal eigenvalue of these operators.

Description

Keywords

Non-local, Uniformly elliptic, Eigenvalues, Multiplicities

Citation

Davidson, F. A., & Dodds, N. (2006). Spectral properties of non-local uniformly-elliptic operators. Electronic Journal of Differential Equations, 2006(126), pp. 1-15.

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Attribution 4.0 International

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