On Existence of Global Solutions of Second-Order Quasilinear Elliptic Inequalities

We study the existence of global positive solutions of the differential inequalities -divA(x,u,∇ u) ≥ f(u) in Rⁿ, where n≥ 2 and A is a Carathéodory function such that gathered \, (A(x,s,ζ)-A (x,s,ξ))(ζ-ξ)≥ 0, \\ C₁|ξ|ᵖ ≤ξ A(x,s,ξ), |A(x,s,ξ)| ≤ C₂|ξ|ᵖ⁻¹, C₁,C₂>0, p>1, gathered for almost all x∈ Rⁿ and all s∈ R and ζ,ξ∈ Rⁿ .