Abstract and Applied Analysis
Volume 2011 (2011), Article ID 340796, 15 pages
http://dx.doi.org/10.1155/2011/340796
Research Article

Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients

Bing Xie and Jian Gang Qi

Department of Mathematics, Shandong University at Weihai, Weihai 264209, China

Received 23 February 2011; Accepted 27 April 2011

Academic Editor: Nicholas D. Alikakos

Copyright © 2011 Bing Xie and Jian Gang Qi. 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

This paper gives sufficient and necessary conditions for the classification of Sturm-Liouville differential equations with complex coefficients given by Brown et al. These conditions involve weighted Sobolev subspaces and the asymptotic behavior of elements in the maximal domain. The results of the present paper generalize the corresponding results for formally symmetric Sturm-Liouville differential equations to non-self-adjoint cases.