Large Solutions to Elliptic Systems of $\infty$-Laplacian Equations

In this paper, we study the existence, uniqueness and boundary behavior of positive boundary blow-up solutions to the quasilinear system $\Delta_{\infty}u=a(x)u^{p}v^{q}$, $\Delta_{\infty}v=b(x)u^{r}v^{s}$ in a smooth bounded domain $\Omega\subset R^{N}$, with the explosive boundary condition $u=v=+\infty$ on $\partial\Omega$, where the operator $\Delta_{\infty}$ is the $\infty$-Laplacian, the positive weight functions $a(x)$, $b(x)$ are Hölder continuous in $\Omega$, and the exponents verify $p$, $s > 3$, $q$, $r>0$, and $(p-3)(s-3) > qr$.