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Removable singularity of positive solutions for a critical elliptic system with isolated singularity

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Abstract

We study qualitative properties of positive singular solutions to a two-coupled elliptic system with critical exponents. This system is related to coupled nonlinear Schrödinger equations with critical exponents for nonlinear optics and Bose-Einstein condensates. We prove a sharp result on the removability of the same isolated singularity for both two components of the solutions. We also prove the nonexistence of positive solutions with one component bounded near the singularity and the other component unbounded near the singularity. These results will be applied in a subsequent work where the same system in a punctured ball will be studied.

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Acknowledgments

The authors wish to thank the anonymous referees very much for their careful reading and valuable comments.

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Authors and Affiliations

  1. Center for Advanced Study in Theoretical Sciences, National Taiwan University, Taipei, 106, Taiwan

    Zhijie Chen

  2. Center for Advanced Study in Theoretical Sciences, Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, 106, Taiwan

    Chang-Shou Lin

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  1. Zhijie Chen
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  2. Chang-Shou Lin
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Correspondence to Chang-Shou Lin.

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Chen, Z., Lin, CS. Removable singularity of positive solutions for a critical elliptic system with isolated singularity. Math. Ann. 363, 501–523 (2015). https://doi.org/10.1007/s00208-015-1177-0

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  • DOI: https://doi.org/10.1007/s00208-015-1177-0

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