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On eigenfunction expansions for a nonlinear Sturm-Liouville operator with spectral-parameter dependent boundary conditions

On eigenfunction expansions for a nonlinear Sturm-Liouville operator with spectral-parameter... We study a nonlinear eigenvalue problem for a Sturm-Liouville operator on the interval (0, 1). The boundary conditions posed at both endpoints of the interval depend on the spectral parameter. We prove that the problem has an eigenfunction system that is a basis in the space L p (0, 1) for p > 1 and a Riesz basis for p = 2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On eigenfunction expansions for a nonlinear Sturm-Liouville operator with spectral-parameter dependent boundary conditions

Differential Equations , Volume 48 (2) – Apr 14, 2012

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266112020024
Publisher site
See Article on Publisher Site

Abstract

We study a nonlinear eigenvalue problem for a Sturm-Liouville operator on the interval (0, 1). The boundary conditions posed at both endpoints of the interval depend on the spectral parameter. We prove that the problem has an eigenfunction system that is a basis in the space L p (0, 1) for p > 1 and a Riesz basis for p = 2.

Journal

Differential EquationsSpringer Journals

Published: Apr 14, 2012

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