Lyapunov type inequality for extremal Pucci's equations

In this article, we establish Lyapunov type inequality for the following extremal Pucci’s equation \begin{equation*} \left{ \begin{aligned}{} $\mathcal{M}$^{+}_{\lambda,\Lambda}(D^{2}u)+a(x)u&=0~$\text{in}$~\Omega,\ u&=0~$\text{on}$~\partial\Omega, \end{aligned} \right. \end{equation*} where $\mathrm{\Omega }$ is a smooth bounded domain in ${\mathbb{R}}^N,N\ge 2$. This works generalize the well-known works on Lyapunov inequalities to fully nonlinear elliptic equations.