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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

On the Existence of Stationary Solutions for Some Systems of Integro-Differential Equations with Anomalous Diffusion

Discontinuity, Nonlinearity, and Complexity 5(3) (2016) 285--295 | DOI:10.5890/DNC.2016.09.007

Vitali Vougalter$^{1}$, Vitaly Volpert$^{2}$

$^{1}$ Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4, Canada

$^{2}$ Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France

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Abstract

The article is devoted to the proof of the existence of solutions of a system of integro-differential equations appearing in the case of anomalous diffusion when the negative Laplacian is raised to some fractional power. The argument relies on a fixed point technique. Solvability conditions for elliptic operators without Fredholm property in unbounded domains along with the Sobolev inequality for a fractional Laplace operator are being used.

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