Science China Mathematics

, Volume 54, Issue 2, pp 243–256

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


    • School of Mathematics and StatisticsSouth-Central University For Nationalities
  • ShuangJie Peng
    • School of Mathematics and StatisticsCentral China Normal University

DOI: 10.1007/s11425-010-4131-3

Cite this article as:
Kang, D. & Peng, S. Sci. China Math. (2011) 54: 243. doi:10.1007/s11425-010-4131-3


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.


elliptic systemnontrivial solutioncritical exponentvariational method


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© Science China Press and Springer-Verlag Berlin Heidelberg 2011