A Liouville theorem for the p-Laplacian and related questions

  • Alberto Farina
  • Carlo MercuriEmail author
  • Michel Willem


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 \({{\mathbb {R}}}^N\) involving critical nonlinearities. Moreover, on radial domains we characterise the compactness of possibly sign-changing Palais–Smale sequences.

Mathematics Subject Classification

35J92 (35B33 · 35B53 · 35B38) 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LAMFA, CNRS UMR 7352, Faculté des SciencesUniversité de Picardie Jules VerneAmiens Cedex 1France
  2. 2.Department of Mathematics, Computational FoundrySwansea UniversitySwanseaUK
  3. 3.Département de MathématiquesUniversité catholique de LouvainLouvain-la-NeuveBelgium

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