On the existence of explosive solutions for semilinear elliptic problems (Q1348213)

This paper deals with the model problem \[ \Delta u= k(x)f(u),\quad u> 0,\quad x\in\Omega,\quad u|_{\partial\Omega}= \infty,\tag{1} \] where \(\Omega\) is a domain in \(\mathbb{R}^N\) \((N> 2)\), and the functions \(k\) and \(f\) satisfy certain conditions. The authors extend the results of both Lair and Wood, Lazar and McKenna, and construct the lowest explosive subsolution of problem (1) with more general \(k(x)\) and \(f(s)\). In addition, when \(\Omega= \mathbb{R}^N\), the authors prove that problem (1) has an entire solution \(u\in C^2(\mathbb{R}^N)\) for more general \(f(s)\).