Solvability of boundary value problems for operator-differential equations of mixed type: the degenerate case

We obtain some results on solvability of boundary value problems for the equation $Bu_t- Lu= f (t\in(0,\infty))$, where $B$ and $L$ are selfadjoint and dissipative operators defined in a Hilbert space $E$. The kernel of $B$ may be nontrivial and $L$ is uniformly dissipative on a subspace $M$ of finite codimension.