On a Dini Type Blow-Up Condition for Solutions of Higher Order Nonlinear Differential Inequalities

We obtain a Dini type blow-up condition for solutions of the differential inequality \(\sum\limits_{|\alpha | = m} {{\partial }^{\alpha }}{{a}_{\alpha }}(x,u) \geqslant g({\text{|}}u{\text{|)}}\;{\text{in}}\;{\kern 1pt} {{\mathbb{R}}^{n}},\) where \(m,n \geqslant 1\) are integers and \({{a}_{\alpha }}\) and g are some functions.