Spectral properties of non-local uniformly-elliptic operators




Davidson, Fordyce A.
Dodds, Niall

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Texas State University-San Marcos, Department of Mathematics


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.



Non-local, Uniformly elliptic, Eigenvalues, Multiplicities


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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