Irregular boundary value problems for elliptic differential-operator equations with discontinuous coefficients and transmission conditions

We consider an irregular boundary value problem with elliptic differential-operator equations of the second order together with multipoint boundary-transmission conditions, including (usually) unbounded operators in a Hilbert space H. In this problem, operators are discontinuous at the zero point and differential equations contain a spectral parameter. We prove coerciveness and Fredholmness of the boundary value problems with a defect, transmission and multipoint conditions.