Vitaly Volpert, Vitali Vougalter
Abstract:
We study the solvability of certain linear nonhomogeneous
elliptic problems and show that under reasonable technical conditions the
convergence in
of their right sides implies the
existence and the convergence in
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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