Abstract
The approach to abstract conjugation boundary-value problems developed in [18] is applied to one-domain and two-domain spectral conjugation problems. An operator pencil with self-adjoint operator coefficients acting in a Hilbert space and depending on two parameters arises; we study it in detail. Both possible cases (where one parameter is the spectral one, while the other one is fixed) are considered; we deduce the corresponding properties of the solutions. Also, we study the initial-value problems of mathematical physics generating conjugation problems. We obtain existence and uniqueness theorems for strong solutions valued in the correspondent Hilbert spaces.
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