On Solvability of Boundary Value Problems for Kinetic Operator-Differential Equations

We study solvability of boundary value problems for the so-called kinetic operator-differential equations of the form B(t)u (t) -L(t)u = f, where L(t) and B(t) are families of linear operators defined in a complex Hilbert space E. We do not assume that the operator B is invertible and that the spectrum of the pencil L -lambda B is included into one of the half-planes Re lambda < a or Re lambda > a . Under certain conditions on the above operators, we prove several existence and uniqueness theorems and study smoothness questions in weighted Sobolev spaces for solutions.