Abstract
Differential inequalities of the form \(- \operatorname{div} A (x, \nabla u)\ge f(u)\quad \text{in}\quad {\mathbb R}^n\) are considered, where \(n \ge 2\) and \(A\) is a Carathéodory function that satisfies the uniform ellipticity conditions \(C_1|\xi|^p\le\xi A (x, \xi), \qquad |A (x, \xi)| \le C_2 |\xi|^{p-1}, \qquad C_1, C_2 > 0, \qquad p > 1,\) for almost every \(x \in {\mathbb R}^n\) and all \(\xi \in {\mathbb R}^n\) . For nonnegative solutions of these inequalities, precise conditions for the absence of nontrivial solutions are obtained.
