Multiplicity results for fully nonlinear elliptic equations with natural gradient growth

In this paper, we prove a theorem concerning the existence of three solutions for the following boundary value problem: {equation*} -Mλ,Λ^+(D^2u)-Γ|Du|^2=f(u)~~~in\ Ω, u=0~~~on\ ∂Ω, {equation*} where f:[0,∞]→[0,∞] is a Cα function and Ω denotes a bounded, smooth domain in RN. By constructing two ordered pairs of sub and supersolutions for a specific class of f exhibiting sublinear growth, we further establish the existence of three positive solutions to the aforementioned boundary value problem.