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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 571951, 9 pages
http://dx.doi.org/10.1155/2012/571951
Research Article

Strict Monotonicity and Unique Continuation for the Third-Order Spectrum of Biharmonic Operator

Department of Mathematics and Computer Science, Faculty of Science, University Mohammed Premier, 60050 Oujda, Morocco

Received 28 September 2012; Accepted 5 November 2012

Academic Editor: Julio Rossi

Copyright © 2012 Khalil Ben Haddouch et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We will study the spectrum for the biharmonic operator involving the laplacian and the gradient of the laplacian with weight, which we call third-order spectrum. We will show that the strict monotonicity of the eigenvalues of the operator , where , holds if some unique continuation property is satisfied by the corresponding eigenfunctions.