Extensions of the matrix-valued q−Sturm–Liouville operators

Abstract

In this paper, we investigate the matrix-valued$\ q-$Sturm--Liouville problems. We establish an existence and uniqueness result. Later, we introduce the corresponding maximal and minimal operators for this system. Moreover, we give a criterion under which these operators are self-adjoint. Finally, we characterize extensions (maximal dissipative, maximal accumulative, and self-adjoint) of the minimal symmetric operator.