Electron. J. Diff. Equ., Vol. 2013 (2013), No. 160, pp. 1-16.

Solvability in the sense of sequences to some non-Fredholm operators

Vitaly Volpert, Vitali Vougalter

We study the solvability of certain linear nonhomogeneous elliptic problems and show that under reasonable technical conditions the convergence in $L^2(\mathbb{R}^d)$ of their right sides implies the existence and the convergence in $H^2(\mathbb{R}^d)$ of the solutions. The equations involve second order differential operators without Fredholm property and we use the methods of spectral and scattering theory for Schrodinger type operators analogously to our preceding work [17].

Submitted March 8, 2013. Published July 12, 2013.
Math Subject Classifications: 35J10, 35P10, 47F05
Key Words: Solvability conditions; non Fredholm operators; Sobolev spaces.

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Vitaly Volpert
Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1
Villeurbanne, 69622, France.
Department of Mathematics, Mechanics and Computer Science
Southern Federal University Rostov-on-Don, Russia
email: volpert@math.univ-lyon1.fr
Vitali Vougalter
Department of Mathematics and Applied Mathematics
University of Cape Town
Private Bag, Rondebosch 7701, South Africa
email: Vitali.Vougalter@uct.ac.za

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