Let Rn be an n-dimensional real Euclidean space with the norm j
j. Let us consider a differential equation u0 = f(t; u); (1) where f 2 C(R  Rn;Rn). Along with equation (1) we consider its Hclass, i.e., the family of equations v0 = g(t; v); (2) where g 2 H(f) = ff :  2 Rg, f (t; u) = f(t + ; u) for all (t; u) 2 R  Rn and by bar we denote the closure in C(R  Rn;Rn). Condition (A1). The function f is said to be regular if for every equation (2) the conditions of existence, uniqueness and extendability on R+ are fulfilled. Let Rn + := fx 2 Rn : such that xi  0 (x := (x1; : : : ; xn)) for any i = 1; 2; : : : ; ng be the cone of nonnegative vectors of Rn. By Rn + on the space Rn is defined a partial order. Namely: u  v if v  u 2 Rn +. Condition (A2). Equation (1) is monotone. This means that the cocycle hRn; '; (H(f); R; )i (or shortly ') generated by (1) is monotone, i.e., if u; v 2 Rn and u  v then '(t; u; g)  '(t; v; g) for all t  0 and g 2 H(f). Condition (A3). fi(t; x)  0 for all x 2 ?i, t 2 R and i = 1; : : : ; n, where Гi := fx 2 Rn + : xi = 0g.