Abstract. We continue a study of the mathematical model of forest ecosystem which has been introduced by Kuznetsov et al. [3]. In this paper, we will introduce three kinds of o-limit sets, namely, oðU 0 Þ H L 2 -oðU 0 Þ H w à -oðU 0 Þ, for each point U 0 of the dynamical system which was constructed in our preceding paper [1]. Using a Lyapunov function, we will then investigate basic properties of these o-limit sets.Especially it shall be shown that L 2 -oðU 0 Þ consists of stationary solutions alone.

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, the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions.2000 Mathematics Subject Classification. 35J60, 37L15, 37N25.