JournalsaihpcVol. 36, No. 6pp. 1575–1601

Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent

  • Almir Silva Santos

    Department of Mathematics, Federal University of Sergipe, 49100-000, São Cristovão-SE, Brazil

  • Rayssa Caju

    Department of Mathematics, Federal University of Paraíba, 58051-900, João Pessoa-PB, Brazil

  • João Marcos do Ó

    Department of Mathematics, Brasília University, 70910-900, Brasília, DF, Brazil
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent cover

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Abstract

We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a rotationally symmetric Fowler type solution. This result generalizes the celebrated work due to Caffarelli, Gidas and Spruck [1] who studied asymptotic proprieties to the classic Yamabe equation. In addition, we generalize similar results by Marques [12] for inhomogeneous context, that is, when the metric is not necessarily conformally flat.

Cite this article

Almir Silva Santos, Rayssa Caju, João Marcos do Ó, Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 6, pp. 1575–1601

DOI 10.1016/J.ANIHPC.2019.02.001