Abstract:
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
$(p-3)(s-3) > qr$.
Keywords:boundary behavior, quasilinear elliptic system, large solution.
