On the Existence of Positive Solutions of Semilinear Elliptic Inequalities on Riemannian Manifolds

  • Alexander Grigor’yan
  • Vladimir A. Kondratiev
Part of the International Mathematical Series book series (IMAT, volume 12)


We consider elliptic inequalities of type ∆u + u σ on geodesically complete Riemannian manifolds and prove sharp suficient conditions in terms of capacities and volumes for the nonexistence of positive solutions.


Riemannian Manifold Sobolev Space Erential Equation Harnack Inequality Complete Riemannian Manifold 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Alexander Grigor’yan
    • 1
  • Vladimir A. Kondratiev
    • 2
  1. 1.Department of MathematicsUniversity of BielefeldBielefeldGermany
  2. 2.Department of MathematicsMoscow State UniversityMoscowRussia

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