Dynamics of Partial Differential Equations

Volume 12 (2015)

Number 1

Existence of stationary solutions for some nonlocal reaction-diffusion equations

Pages: 43 – 51

DOI: https://dx.doi.org/10.4310/DPDE.2015.v12.n1.a3

Authors

Vitali Vougalter (Department of Mathematics, University of Toronto, Ontario, Canada)

Vitaly Volpert (Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, France)

Abstract

The paper is devoted to the existence of solutions of a nonlocal reaction-diffusion equation arising in population dynamics. The proof is based on a fixed point technique. We use solvability conditions for elliptic operators in unbounded domains which do not satisfy the Fredholm property.

Keywords

nonlinear heat equations, non-Fredholm operators, Sobolev spaces

2010 Mathematics Subject Classification

Primary 35J05. Secondary 35P30, 47F05.

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Published 19 March 2015