| Summary: | In this article we study the blow-up rate of solutions
near the boundary for the semilinear elliptic problem
$$\displaylines{
\Delta u\pm |\nabla u|^q=b(x)f(u), \quad x\in\Omega,\cr
u(x)=\infty, \quad x\in\partial\Omega,
}$$
where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, and b(x) is a
nonnegative weight function which may be bounded or singular on
the boundary, and f is a regularly varying function at infinity.
The results in this article emphasize the central role played by
the nonlinear gradient term $|\nabla u|^q$ and the singular weight b(x).
Our main tools are the Karamata regular variation theory and the method of
explosive upper and lower solutions.
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