Variational Equations of Schroedinger-Type in Non-cylindrical Domains

Cauchy-Dirichlet problems are studied for linear Schroedinger-type partial differential equations in non–cylindrical domains by assuming a monotonicity condition on their sections with respect to time. Existence and uniqueness results are obtained as a consequence of new general results that we prove here for a class of abstract Schroedinger-type differential equations in Hilbert spaces.