  The selfconsistent steady state solution for a strong shock, significantly
modified by accelerated particles is obtained on the level of a kinetic
description, assuming Bohm-type diffusion. The original problem that is
commonly formulated in terms of the diffusion-convection equation for the
distribution function of energetic particles, coupled with the thermal plasma
through the momentum flux continuity equation, is reduced to a nonlinear
integral equation in one variable. Its solution provides selfconsistently both
the particle spectrum and the structure of the hydrodynamic flow. A critical
system parameter governing the acceleration process is found to be $\Lambda =
M^{-3/4}\Lambda_1 $, where $ \Lambda_1 =\eta p_1/mc $, with a suitably
normalized injection rate $ \eta $, the Mach number M >> 1, and the cut-off
momentum $ p_1 $. We particularly focus on an efficient solution, in which
almost all the energy of the flow is converted into a few energetic particles.
It was found that (i) for this efficient solution (or, equivalently, for
multiple solutions) to exist, the parameter $ \zeta =\eta\sqrt{p_0 p_1}/mc $
must exceed a critical value $\zeta_{cr} \sim 1$ ($p_0$ is the injection
momentum), (ii) the total shock compression ratio r increases with M and
saturates at a level that scales as $ r \propto \Lambda_1 (iii) the downstream
power-law spectrum has the universal index q=3.5 over a broad momentum range.
(iv) completely smooth shock transitions do not appear in the steady state
kinetic description.
