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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 Non-Fredholm Integro-Differential Equations

Discontinuity, Nonlinearity, and Complexity 1(2) (2012) 197--209 | DOI:10.5890/DNC.2012.05.003

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

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

$^{2}$ Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag Rondebosch 7701, South Africa.

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Abstract

We prove the existence of stationary solutions for certain systems of reaction-diffusion type equations in the corresponding H2 spaces. Our method relies on the fixed point theorem when the elliptic problem involves second order differential operators with and without Fredholm property.

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