Some Liouville-type results for stable solutions involving the mean curvature operator: The radial case

Abstract

We prove some new Liouville-type theorems for stable radial solutions of \begin{document}$ - {{\rm{div}}}{\left(\frac{\nabla u}{\sqrt{1+\left\vert{\nabla u}\right\vert^2}}\right)} = f(u)\mbox{ in } \mathbb R^N, $\end{document} where \begin{document}$ f $\end{document} is a smooth nonlinearity and \begin{document}$ N \ge 2 $\end{document} . Also, the sharpness of our results is discussed by means of some examples.