Annales Henri Poincaré

, Volume 14, Issue 4, pp 947–966 | Cite as

On a General Class of Nonlocal Equations

  • Przemysław Górka
  • Humberto Prado
  • Enrique G. Reyes
Article
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Abstract

Motivated by recent developments in cosmology and string theory, we introduce a functional calculus appropriate for the study of non-linear nonlocal equations of the form f(Δ)u = U(x, u(x)) on Euclidean space. We prove that under some technical assumptions, these equations admit smooth solutions. We also consider nonlocal equations on compact Riemannian manifolds, and we prove the existence of smooth solutions. Moreover, in the Euclidean case we present conditions on f which guarantee that the solutions we find are, in fact, real-analytic.

Keywords

Riemannian Manifold High Energy Phys Radial Function Pseudodifferential Operator Functional Calculus 
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Przemysław Górka
    • 1
  • Humberto Prado
    • 2
  • Enrique G. Reyes
    • 2
  1. 1.Department of Mathematics and Information SciencesWarsaw University of TechnologyWarsawPoland
  2. 2.Departamento de Matemática y Ciencia de la ComputaciónUniversidad de Santiago de ChileSantiagoChile

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