  We consider "forward-backward" parabolic equations in the abstract form $Jd
\psi / d x + L \psi = 0$, $ 0< x < \tau \leq \infty$, where $J$ and $L$ are
operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and
$\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is
similar to a self-adjoint operator, then associated half-range boundary
problems have unique solutions. We apply this theorem to corresponding
nonhomogeneous equations, to the time-independent Fokker-Plank equation $ \mu
\frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2
\psi}{\partial \mu^2} (x, \mu)$, $ 0<x<\tau$, $ \mu \in \R$, as well as to
other parabolic equations of the "forward-backward" type. The abstract kinetic
equation $ T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and
$A$ satisfies a certain positivity assumption, is considered also.
