On the pure critical exponent problem for the p-Laplacian

2012/06/19 by Carlo Mercuri, Mercuri, Carlo, Filomena Pacella +1
Computer Science · Mathematics · #35J20 #35J66 #35J92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1206.4341

openalex publication_date 2012/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove existence and multiplicity of positive and sign-changing solutions to the pure critical exponent problem for the p-Laplacian operator with Dirichlet boundary conditions on a bounded domain having nontrivial topology and discrete symmetry. Pioneering works related to the case p=2 are H. Brezis and L. Nirenberg [4], J.-M. Coron [10], and A. Bahri and J.-M. Coron [3]. A global compactness analysis is given for the Palais-Smale sequences in the presence of symmetries.

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