Existence of blowup solutions for nonlinear problems with a gradient term (Q885614)

Summary: We prove the existence of positive explosive solutions for the equation \[ Au+\lambda(|x|)|\nabla u(x)|=\varphi(x, u(x)) \] in the whole space \(\mathbb{R}^N\) \((N\geq 3)\), where \(\lambda: [0,\infty)\to [0,\infty)\) is a continuous function and \(\varphi:\mathbb{R}^N\times[0, \infty)\to [0,\infty)\) is required to satisfy some particular hypotheses. More precisely, we give a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.