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

We consider systems of the differential inequalities $$\{\begin{array}{rlrlr}{\displaystyle }& {\displaystyle \sum _{\mathrm{\mid }\alpha \mathrm{\mid }=m_1}{\mathrm{\partial }}^{\alpha }{a}_{\alpha }(x,u_1)\ge f_1(u_2)}& {\displaystyle in{\mathbb{R}}^n,}& {\displaystyle \sum _{\mathrm{\mid }\alpha \mathrm{\mid }=m_2}{\mathrm{\partial }}^{\alpha }{b}_{\alpha }(x,u_2)\ge f_2(u_1)}& {\displaystyle in{\mathbb{R}}^n,}\end{array}$$ where $n,m_1,m_2\ge 1$ are integers and $a_{\alpha }$ and $b_{\alpha }$ are Caratheodory functions such that $$\mathrm{\mid }{a}_{\alpha }(x,\zeta )\mathrm{\mid }+\mathrm{\mid }{b}_{\alpha }(x,\zeta )\mathrm{\mid }\le A\mathrm{\mid }\zeta \mathrm{\mid }$$ with some constant $A>0$ for almost all $x\in {\mathbb{R}}^n$ and for all $\zeta \in \mathbb{R}$. For solutions of these systems exact blow-up conditions are obtained.