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Existence and asymptotic properties of solutions to elliptic systems involving multiple critical exponents

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Abstract

This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.

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Authors and Affiliations

  1. School of Mathematics and Statistics, South-Central University For Nationalities, Wuhan, 430074, China

    DongSheng Kang

  2. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    ShuangJie Peng

Authors
  1. DongSheng Kang
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  2. ShuangJie Peng
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Correspondence to DongSheng Kang.

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Kang, D., Peng, S. Existence and asymptotic properties of solutions to elliptic systems involving multiple critical exponents. Sci. China Math. 54, 243–256 (2011). https://doi.org/10.1007/s11425-010-4131-3

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  • DOI: https://doi.org/10.1007/s11425-010-4131-3

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