On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds

  • Alexander Grigor’yan
  • Yuhua SunEmail author


We determine the critical exponent for certain semi-linear elliptic problem on a Riemannian manifold assuming the volume regularity and Green function estimates.

Mathematics Subject Classification

Primary 58J05 Secondary 35J61 



The authors would like to express their deep gratitude to the late Prof. Vladimir A. Kondratiev who initiated the study of the above problems. The authors are indebted to Prof. Igor Verbitsky for helpful discussions on the subject of the paper. The authors are also grateful to the anonymous referee for useful comments.


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Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of BielefeldBielefeldGermany

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