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

Solvability Conditions For Some Non Fredholm Operators in a Layer in Four Dimensions

Discontinuity, Nonlinearity, and Complexity 3(1) (2014) 59--71 | DOI:10.5890/DNC.2014.03.005

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

Abstract

We study solvability in H2 of certain linear nonhomogeneous elliptic prob- lems involving the sum of the periodic Laplacian and a Schrödinger oper- ator without Fredholm property and prove that under reasonable technical conditions the convergence in L2 of their right sides implies the existence and the convergence in H2 of the solutions. We generalize the methods of spectral and scattering theory for Schro ̈dinger type operators from our preceding work [1].

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