Existence of Blow-up Solutions of Semilinear Elliptic Problems

Abstract

We consider the boundary blow-up nonlinear elliptic problems \(\Delta u \pm \lambda |\nabla u|^\beta = k(x) f(u)\) in a smooth bounded domain \( D\subset \mathbb R ^N\), with \(u|_{\partial D}=\infty \), where \(\beta \in [0,2)\) and \(\lambda \ge 0.\) Under suitable assumptions on \(k\) and \(f\), we show the existence of at least one solution \(u\).