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A Liouville theorem for the p-Laplacian and related questions

Alberto Farina, Carlo Mercuri Orcid Logo, Michel Willem

Calculus of Variations and Partial Differential Equations, Volume: 58, Issue: 4

Swansea University Author: Carlo Mercuri Orcid Logo

Abstract

We obtain several classification results for p-Laplacian problems on bounded and unbounded domains, and deal with qualitative properties of sign-changingsolutions to p-Laplacian equations involving critical growth nonlinearities. Some of these are derived by the Morse index associated with the solut...

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Published in: Calculus of Variations and Partial Differential Equations
ISSN: 0944-2669 1432-0835
Published: 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa51017
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Abstract: We obtain several classification results for p-Laplacian problems on bounded and unbounded domains, and deal with qualitative properties of sign-changingsolutions to p-Laplacian equations involving critical growth nonlinearities. Some of these are derived by the Morse index associated with the solutions. These resuts, in a radial setting allow to characterise the compactness of possibly sign-changing Palais-Smale sequences.
Keywords: Liouville-type theorems, quasilinear equations, Morse index, sign-changing solutions, nonexistence, Palais-Smale sequences
College: College of Science
Issue: 4