On bow-up conditions for systems of higher order differential inequalities

We consider systems of the differential inequalities $$\{ {aligned} & ∑|α| = m_1 ∂^αa_α(x, u_1) ≥ f_1 (u_2) & in { R}^n, & ∑|α| = m_2 ∂^αb_α(x, u_2) ≥ f_2 (u_1) & in { R}^n, {aligned} . $$ where $n, m_1, m_2 ≥ 1$ are integers and $a_α$ and $b_α$ are Caratheodory functions such that $$ |a_α(x, ζ)| + |b_α(x, ζ)| ≤ A |ζ| $$ with some constant $A > 0$ for almost all $x ∈ { R}^n$ and for all $ζ∈ { R}$. For solutions of these systems exact blow-up conditions are obtained.