On the inequality $F(x,D^2u) \geq f(u)+g(u)|Du|^q$

TL;DR

This paper studies fully nonlinear degenerate elliptic equations with zero and first order terms, establishing a priori bounds and conditions for entire subsolutions, extending classical Keller-Osserman results.

Contribution

It extends the Keller-Osserman condition to a broader class of fully nonlinear equations with growth conditions on coefficients.

Findings

Derived a priori upper bounds for solutions.

Characterized existence of entire subsolutions.

Extended classical Keller-Osserman conditions.

Abstract

We consider fully nonlinear degenerate elliptic equations with zero and first order terms. We provide a priori upper bounds and characterize the existence of entire subsolutions under growth conditions on the lower order coefficients which extend the classical Keller--Osserman condition for semilinear equations.