Regular boundary value problems with a discontinuous coefficient, functional-multipoint conditions, and a linear spectral parameter

Abstract

We consider a linear differential equation which includes a linear abstract operator, with a piecewise constant coefficient at the principal differential term, together with multipoint boundary-transmission conditions, including linear functionals. The spectral parameter appears linearly in the equation and may appear also linearly in the boundary-transmission conditions. We prove an isomorphism and coerciveness of the problem with respect to the spectral parameter and the space variable.