Abstract
In this paper, we study the asymptotic behavior of viscosity solutions to boundary blow-up elliptic problem $${\Delta_{\infty}u=b(x)f(u),\, x\in\Omega,\,u|_{\partial\Omega}=+\infty,}$$ where $${\Omega}$$ is a bounded domain with C 2-boundary in $${\mathbb{R}^{N}}$$ , $${b\in \rm C(\bar{\Omega})}$$ is positive in $${\Omega}$$ , which may be vanishing on the boundary, $${f\in C^{1}([0, \infty))}$$ is regularly varying or is rapidly varying at infinity.
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