Sturm-Liouville Abstract Problems for the Second Order Differential Equations in a Non Commutative Case

Abstract

In this paper we prove some new results on Sturm-Liouville abstract problems of the second order differential equations of elliptic type in a new non-commutative framework. We study the case when the second member belongs to a Sobolov space. Existence, uniqueness and optimal regularity of the strict solution are proved. This paper is naturally the continuation of the ones studied by Cheggag et al in the commutative case. We also give an example to which our theory applies.