Dissipative boundary value problems for symmetric differential systems with degenerating weights

Abstract

Since symmetric systems of differential equations of arbitrary even or odd order and some difference equations can be reduced to a system of the form (1), our results automatically extend to boundary value problems for these systems. Dissipative boundary value problems arise, e.g, in the theory of oscillations. Our description of boundary conditions is based not on the traditional use of the theory of Hermitian and maximal dissipative relations (see e.g. [1, 2]), but on the parametrization of maximal semidefinite subspaces in a space with a special indefinite metric.