A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient (Q2178810)

The authors show a Liouville-type result for solutions of the problem \(-\Delta u = u^{q}|\nabla u|^{p}\) in \(\mathbb{R}^{N}\), where \(p>2\), \(q>0\) and \(N\geq 1\). The basic idea of the proof is to the use monotonicity property of a supersolution and of a subsolution of the problem.