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arXiv · 1206.4341

On the pure critical exponent problem for the $p$-Laplacian

Carlo Mercuri·Filomena Pacella
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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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Carlo Mercuri, Filomena Pacella. 2013-01-22. On the pure critical exponent problem for the $p$-Laplacian. https://arxiv.org/abs/1206.4341

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