On blow-up conditions for solutions of a class of second-order elliptic inequalities

We consider the inequality −divA(x,∇u)≥F(x,u)in Rn, where n≥2 and A:R2n→Rn is a Caratheodory function such that C1|ξ|p≤ξA(x,ξ)and|A(x,ξ)|≤C2|ξ|p−1 with some constants C1>0, C2>0, and p>1 for almost all x∈Rn and for all ξ∈Rn. Our aim is to find exact blow-up conditions for solutions of this inequality. © 2025 Elsevier Inc.