no. 1-2
Partial Differential Equations
Multiple symmetric solutions for a Neumann problem with lack of compactness
[Solutions symétriques multiples pour un problème de Neumann sans compacité]

Présenté par : Philippe G. Ciarlet

Molica Bisci, Giovanni1 ; Rădulescu, Vicenţiu2, 3
1 Dipartimento MECMAT, University of Reggio Calabria, Via Graziella, Feo di Vito, 89124 Reggio Calabria, Italy
2 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 014700 Bucharest, Romania
3 Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova, Romania
Comptes Rendus. Mathématique, Tome 351 (2013) no. 1-2, pp. 37-42.

On étudie lʼexistence de solutions multiples à symétrie cylindrique pour une classe de problèmes elliptiques non autonomes de Neumann sans compacité. La preuve combine un résultat récent de compacité et le principe de Palais de symétrique critique. Une application met en évidence le résultat principal de cette Note.

The existence of multiple cylindrically symmetric solutions for a class of non-autonomous elliptic Neumann problems in a strip-like domain of the Euclidean space is investigated. The proof combines a recent compactness result and the Palais symmetric critically principle. A concrete application illustrates the main abstract result of this Note.

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DOI : 10.1016/j.crma.2012.12.001
Molica Bisci, Giovanni 1 ; Rădulescu, Vicenţiu 2, 3

1 Dipartimento MECMAT, University of Reggio Calabria, Via Graziella, Feo di Vito, 89124 Reggio Calabria, Italy
2 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 014700 Bucharest, Romania
3 Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova, Romania 
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Molica Bisci, Giovanni; Rădulescu, Vicenţiu. Multiple symmetric solutions for a Neumann problem with lack of compactness. Comptes Rendus. Mathématique, Tome 351 (2013) no. 1-2, pp. 37-42. doi : 10.1016/j.crma.2012.12.001. http://www.numdam.org/articles/10.1016/j.crma.2012.12.001/

[1] Bonanno, G.; Marano, S.A. On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., Volume 89 (2010), pp. 1-10

[2] Faraci, F.; Iannizzotto, A.; Kristály, A. Low-dimensional compact embeddings of symmetric Sobolev spaces with applications, Proc. Roy. Soc. Edinburgh Sect. A, Volume 141 (2011), pp. 383-395

[3] Palais, R.S. The principle of symmetric criticality, Commun. Math. Phys., Volume 69 (1979), pp. 19-30

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