Boundary Value Problems
Volume 2011 (2011), Article ID 268032, 27 pages
doi:10.1155/2011/268032
Research Article

Degenerate Anisotropic Differential Operators and Applications

Ravi Agarwal,1 Donal O'Regan,2 and Veli Shakhmurov3

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
2Department of Mathematics, National University of Ireland, Galway, Ireland
3Department of Electronics Engineering and Communication, Okan University, Akfirat, Tuzla 34959 Istanbul, Turkey

Received 2 December 2010; Accepted 18 January 2011

Academic Editor: Gary Lieberman

Copyright © 2011 Ravi Agarwal 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

The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued 𝐿 𝑝 spaces are given. Sharp estimates for resolvent, discreetness of spectrum, and completeness of root elements of the corresponding differential operators are obtained. In the last section, some applications of the main results are given.