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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum\limits_{|\alpha | = m} {{\partial }<^>{\alpha }}{{a}_{\alpha }}(x,u) \geqslant g({\text{|}}u{\text{|)}}\;{\text{in}}\;{\kern 1pt} {{\mathbb{R}}<^>{n}},$$\end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m,n \geqslant 1$$\end{document} are integers and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{a}_{\alpha }}$$\end{document} and g are some functions.