A Liouville theorem for the p-Laplacian and related questions

Alberto Farina (1) , Carlo Mercuri , Michel Willem

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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 involving critical nonlinearities. Moreover, on radial domains we characterise the compactness of possibly sign-changing Palais-Smale sequences.

Domaines: Mathématiques [math]

Alberto Farina, Carlo Mercuri, Michel Willem. A Liouville theorem for the p-Laplacian and related questions. Calculus of Variations and Partial Differential Equations, 2019, 58 (4), ⟨10.1007/s00526-019-1596-y⟩. ⟨hal-03621408⟩