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.
Bing Xie. Jian Gang Qi. "Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients." Abstr. Appl. Anal. 2011 1 - 15, 2011. https://doi.org/10.1155/2011/340796