The asymptotic behaviour of solutions with blow-up at the boundary for semilinear elliptic problems (Q2484172)

The aim of this paper is to study the precise asymptotic behaviour of the solutions near the boundary to the model problems \[ \Delta u= k(x)g(u),\quad x\in\Omega, \] \[ u|_{\partial\Omega}= +\infty, \] where \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb{R}^N\) \((N\geq 1)\), \(g\in C^1([0,\infty))\) and satisfies additional natural assumptions.