Generalization of the Keller-Osserman theorem for higher order differential inequalities

We obtain exact conditions guaranteeing that any global weak solution of the differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge g (|u|) \quad \mbox{in } {\mathbb R}^n $$ is trivial, where \(m, n \ge 1\) are integers and \(a_\alpha\) and \(g\) are some functions. These conditions generalize the well-know Keller-Osserman condition.