We continue the study of a mathematical model for the forest ecosystem 
which has been presented by Kuzunetsov et al.~\cite{KuAnBiAp} 
and which is equipped with the Dirichlet boundary conditions. 
In the preceding two papers \cite{ShiChuYa,ShiChuYa2}, 
we constructed a dynamical system and investigated asymptotic behavior of trajectories 
of the dynamical system. This paper is then devoted to studying the stationary problem. 
Stability and instability of the zero stationary solution is investigated. 
When the mortality of trees is suitably small, it is shown by the numerical methods 
that the system possesses a unique inhomogeneous solution which has a clear gap 
which indicates discontinuity of the density of trees.