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.

Keywords

Integro-differential equations Non Fredholm operators Sobolev spaces 

Mathematics Subject Classification

35J05 35P30 47F05 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Institute Camille Jordan, UMR 5208 CNRSUniversity Lyon 1VilleurbanneFrance

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