文摘
The main objective of this paper is to give a classification of Sturm-Liouville differential equations with non-symmetric matrices coefficients in terms of the number of square integrable solutions of the system and its conjugate system. The conjugate system is innovatively introduced to get the classification. Furthermore, the asymptotic behavior of elements in the maximal domain is studied. As applications, the J-self-adjoint operator realizations are given for a special case in the classification.