A Liouville theorem for the p-Laplacian and related questions

We prove several classification results for p-Laplacian problems on bounded and unbounded domains, and deal with qualitative properties of sign-changing solutions to p-Laplacian equations on RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {R}}}^N$$\end{document} involving critical nonlinearities. Moreover, on radial domains we characterise the compactness of possibly sign-changing Palais–Smale sequences.