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A non-variational system involving the critical Sobolev exponent. The radial case

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Abstract

In this paper we consider the non-variational system

$$\begin{cases}-\Delta{u_i}=\Sigma_{j=1}^k\;a_{ij}u_j^{\frac{N+2}{N-2}}\;\;\;\;{\rm{in}} & \mathbb{R}^N,\\u_i>0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{in}}&\mathbb{R}^N,\\u_i\in{D^{1,2}(\mathbb{R}^N)}, \end{cases}$$
(0.1)

and we give some sufficient conditions on thematrix (aij)i, j =1,...,k which ensure the existence of solutions bifurcating from the bubble of the critical Sobolev equation.

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Authors and Affiliations

  1. Dipartimento di Chimica e Farmacia, Università di Sassari, Via Piandanna 4, 07100, Sassari, Italy

    Francesca Gladiali

  2. Dipartimento di Matematica, Università di Roma La Sapienza, P.le A. Moro 2, 00185, Roma, Italy

    Massimo Grossi

  3. Département de Mathématique, Université de Mons, Place du Parc 20, B-7000, Mons, Belgium

    Christophe Troestler

Authors
  1. Francesca Gladiali
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  2. Massimo Grossi
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  3. Christophe Troestler
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Corresponding author

Correspondence to Francesca Gladiali.

Additional information

The first author is supported by Gruppo Nazionale per l′Analisi Matematica, la Probabilitá e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and FABBR.

The first two authors are supported by PRIN-2015KB9WPT.

The third author is partially supported by the project “Existence and asymptotic behavior of solutions to systems of semilinear elliptic partial differential equations” (T.1110.14) of the Fonds de la Recherche Fondamentale Collective, Belgium.

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Gladiali, F., Grossi, M. & Troestler, C. A non-variational system involving the critical Sobolev exponent. The radial case. JAMA 138, 643–671 (2019). https://doi.org/10.1007/s11854-019-0040-8

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  • DOI: https://doi.org/10.1007/s11854-019-0040-8

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