Mathematics of the USSR-Sbornik · 1982 · 12 citations · 1 references
Natural SciencesMathematicsAlgebraDifferential EquationsDynamical SystemsBoundary ConditionsBoundary-value ProblemsHilbert Space FormalismOperator TheoryPartial Differential EquationsSpectral TheoryResolvent OperatorsResolvent Theory
is studied, where , , , and the operators , , which commute with ; act in a Hilbert space and satisfy appropriate (quite strong) requirements formulated in terms of resolvent, or spectral, properties. The character of the boundary conditions with respect to (at ), which are imposed on the equation and ensure existence and uniqueness of the solution, is elucidated, and properties of the solution depending on and on the properties of the operators and are investigated, as well. Bibliography: 7 titles.
1