Comptes Rendus
no. 2
Partial differential equations
Low- and high-energy solutions of nonlinear elliptic oscillatory problems

Presented by: Philippe G. Ciarlet

Giovanni Molica Bisci1; Vicenţiu Rădulescu2, 3; Raffaella Servadei4
1 Dipartimento Patrimonio, Architettura e Urbanistica, University of Reggio Calabria, 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
4 Dipartimento di Matematica e Informatica, Università della Calabria, Ponte Pietro Bucci 31 B, 87036 Arcavacata di Rende, Cosenza, Italy
Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 117-122.

In this Note, we study the existence of low- or high-energy solutions for a class of elliptic problems containing a nonlinear term that oscillates either near the origin or at infinity. We point out the competition effect between the oscillatory nonlinearity, a polynomial growth term, and the values of a real parameter. The proofs combine related variational methods.

Dans cette Note, nous étudions lʼexistence de solutions à basse ou à haute énergie pour une classe de problèmes elliptiques contenant un terme non linéaire oscillatoire autour de lʼorigine ou à lʼinfini. Nous mettons en évidence lʼeffet de compétition entre la non-linéarité oscillatoire, le terme à croissance polynomiale et les valeurs dʼun paramètre réel. Les preuves combinent des méthodes topologiques et variationnelles.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.11.015

Giovanni Molica Bisci 1; Vicenţiu Rădulescu 2, 3; Raffaella Servadei 4

1 Dipartimento Patrimonio, Architettura e Urbanistica, University of Reggio Calabria, 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
4 Dipartimento di Matematica e Informatica, Università della Calabria, Ponte Pietro Bucci 31 B, 87036 Arcavacata di Rende, Cosenza, Italy 
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Giovanni Molica Bisci; Vicenţiu Rădulescu; Raffaella Servadei. Low- and high-energy solutions of nonlinear elliptic oscillatory problems. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 117-122. doi : 10.1016/j.crma.2013.11.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.015/

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[4] G. Molica Bisci, V. Rădulescu, R. Servadei, Competition phenomena for elliptic equations involving a general operator in divergence form, in preparation.

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