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Existence of stationary solutions for some integro-differential equations with anomalous diffusion

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Abstract

The article deals with the existence of solutions of an integro-differential equation arising in population dynamics in the case of anomalous diffusion involving the negative Laplace operator raised to a certain fractional power. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for non-Fredholm elliptic operators in unbounded domains along with the Sobolev inequality for a fractional Laplacian are being used.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada

    Vitali Vougalter

  2. Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622, Villeurbanne, France

    Vitaly Volpert

Authors
  1. Vitali Vougalter
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  2. Vitaly Volpert
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Correspondence to Vitali Vougalter.

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Vougalter, V., Volpert, V. Existence of stationary solutions for some integro-differential equations with anomalous diffusion. J. Pseudo-Differ. Oper. Appl. 6, 487–501 (2015). https://doi.org/10.1007/s11868-015-0128-6

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  • DOI: https://doi.org/10.1007/s11868-015-0128-6

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