$_{u}$′ 1 = u$_{2}$, $_{u}$′ 2 = − u$_{1}$ + 0 . 001 u$_{2}$, Δ u | t = θ$_{2}$$_{i}$$_{−}$$_{1}$ = D (1) 2 $^{i}$− $_{1}$u, Δ u | t = θ$_{2}$$_{i}$ = D (1) 2 i u, (3.29) and $_{u}$′ 1 = u$_{2}$, u ′ 2 = − u$_{1}$ + 0 . 001 u$_{2}$, Δ u | t = θ$_{2}$$_{i}$$_{−}$$_{1}$ = D (2) 2 $^{i}$− $_{1}$u, Δ u | t = θ$_{2}$$_{i}$ = D (2) 2 i u, (3.30) where $^{θ$_{2}$$_{i}$}$− 1 = (2 $^{i}$− 1) π 2 and θ$_{2}$$_{i}$ = iπ The sequences { D ( j ) i } , j = 1 , 2 , are 2 − periodic. It is appearant that system (3.29)+(3.30) is a ( ω, 2) − periodic. Thus, the variational system for the grazing solution is constructed. In this section, we proceed investigation of the grazing periodic solution Ψ( t ) . Analysis of orbital stability will be taken into account. Denote by B ( z, δ ) , an open ball with center at z and the radius δ > 0 for a fixed point z ∈ Γ \ ∂ Γ . By condition (C3), the ball is divided by surface Γ into two connected open regions. Denote c $^{+}$( z, δ ) , for the region, where solution x ( t ) = x ( t, 0 , z ) of (2.2) enters as time increases. The region is depicted in Figure 3. Set the path of the periodic solution Ψ( t ) as Define dist ( A, a $^{) = inf$_{α}$}$∈ A ‖ α − a ‖ , where A is a set, and a is a point. 4 Orbital stability η := { x ∈ D : x = Ψ( t ) , t ∈ $^{R}$} . Figure 3: The region c $^{+}$( z, δ ) . z c (z, δ + ) 20