Fully nonlinear degenerate equations with sublinear gradient term

We establish existence and uniqueness of positive viscosity solutions of P<inf>k</inf>^±(D²u)+|Du|^qu^p=0inΩ,u=0on∂Ω,where k<N,Ω is a bounded domain in R^N,N≥2,0<p<1,0≤q<1 and P<inf>k</inf>^± are degenerate elliptic operators. First, we use of a change of dependent variable originating in Brezis and Kamin (1992) in order to convert the equation into one with the right monotonicity in the u-variable. Thereafter by applying Perron's method, we prove the existence and uniqueness of the solutions. Using an a-priori estimate, we show the nonexistence of subsolutions. We also find the ranges of p and q for the existence and nonexistence results.