On Spectral and Evolutional Problems Generated by a Sesquilinear Form

On the base of boundary-value, spectral and initial-boundary value problems studied earlier for case single domain, we consider corresponding generated by a sesquilinear form two domains. Arising operator pencils with coefficients acting in Hilbert space depending on parameters are detail. In perturbed unperturbed cases, situations where one is other fixed. this paper, use superposition principle that allows us to present solution original problem as sum solutions auxiliary boundary-value containing inhomogeneity either equation or boundary conditions. The necessary sufficient conditions correct solvability given time interval obtained. Theorems properties spectrum completeness basicity system root elements proved.