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Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems

Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems We obtain solvability conditions in $$H^{2}$$ for some elliptic equations in cylindrical domains using the methods of spectral theory and scattering theory for Schrödinger type operators. We prove the existence of standing solitary waves in $$H^{2}$$ for some nonlinear equations. Both linear and nonlinear problems involve second order differential operators without Fredholm property. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel
Subject
Mathematics; Mathematical Methods in Physics; Analysis
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-012-0046-1
Publisher site
See Article on Publisher Site

Abstract

We obtain solvability conditions in $$H^{2}$$ for some elliptic equations in cylindrical domains using the methods of spectral theory and scattering theory for Schrödinger type operators. We prove the existence of standing solitary waves in $$H^{2}$$ for some nonlinear equations. Both linear and nonlinear problems involve second order differential operators without Fredholm property.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Oct 30, 2012

References