Abstract Schroedinger-Type Differential Equations with Variable Domain*

The Cauchy problem is studied for a class of linear abstract differential equations of Schroedinger-type with variable domain. Existence and uniqueness results are proved for suitably defined. weak solutions. Some applications are given: they concern initial-boundary value problems for linear Schroedinger-type P.D.E., either with mixed variable lateral conditions or in non-cylindrical regions