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: \begin{equation*} -$\mathcal{M}$_{λ,Λ}^+(D^2u)-Γ|Du|^2=f(u)~$\text{in}$\ Ω, u=0~$\text{on}$\ \partialΩ, \end{equation*} where $f:[0,\mathrm{\infty }]\to [0,\mathrm{\infty }]$ is a $C^{\alpha }$ function and $\mathrm{\Omega }$ denotes a bounded, smooth domain in ${\mathbb{R}}^N$. 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.