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

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.


Manifold Radon 


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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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