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Open Access Research Article

Degenerate Anisotropic Differential Operators and Applications

Ravi Agarwal1, Donal O'Regan2 and Veli Shakhmurov3*

Author Affiliations

1 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

2 Department of Mathematics, National University of Ireland, Galway, Ireland

3 Department of Electronics Engineering and Communication, Okan University, Akfirat, Tuzla 34959 Istanbul, Turkey

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Boundary Value Problems 2011, 2011:268032  doi:10.1155/2011/268032

Published: 23 February 2011

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 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.