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 Brezis and Nirenberg (Comm Pure Appl Math 36, 437-477, 1983), Coron (C R Acad Sci Paris Sr I Math 299, 209-212, 1984), and Bahri and Coron (Comm. Pure Appl. Math. 41, 253-294, 1988). A global compactness analysis is given for the Palais-Smale sequences in the presence of symmetries. © 2013 Springer-Verlag Berlin Heidelberg.
On the pure critical exponent problem for the p-Laplacian / Mercuri, C.; Pacella, F.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 49:3-4(2014), pp. 1075-1090. [10.1007/s00526-013-0612-x]