Theorem 2. 4 Assume h is continuous and satisfies H(x,A1)-H(x,A2)≤K(1+|x1)A1-A2 95) for all a,A1,A2∈Rn,and H(x1,))-H(x2,川≤(x1-x2,B)+u(x1-x21N,R) for allAE R, 31, r2 E B(O, R),R>0, where w is a modulus( depending on R). Let Vi, V2 E C(to, t]xR)be, respectively, viscosity sub-and supersolution of(7) satisfying V(t1,x)≤V(t1,x)yx∈Rn. V(t,x)≤V2(t,x)(t,x)∈{to,t]×RTheorem 2.4 Assume H is continuous and satisfies |H(x, λ1) − H(x, λ2)| ≤ K(1 + |x|)|λ1 − λ2| (95) for all x, λ1, λ2 ∈ Rn , and |H(x1, λ) − H(x2, λ)| ≤ ω(|x1 − x2|, R) + ω(|x1 − x2||λ|, R) (96) for all λ ∈ Rn , x1, x2 ∈ B(0, R), R > 0, where ω is a modulus (depending on R). Let V1, V2 ∈ C([t0, t1] × Rn ) be, respectively, viscosity sub- and supersolution of (7)’ satisfying V1(t1, x) ≤ V2(t1, x) ∀ x ∈ Rn . (97) Then V1(t, x) ≤ V2(t, x) ∀ (t, x) ∈ [t0, t1] × Rn . (98) 21