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math-phJul 3, 2007
37
citations (OpenAlex)
authors
  • Ph. Choquard
  • J. Stubbe
institutions
  • École Polytechnique Fédérale de Lausanne
arXiv abstractPDF
paper

The one-dimensional Schrödinger-Newton equations

arXiv:0707.0346 · doi:10.1007/s11005-007-0174-y

Abstract

We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equations.

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  • Groundstates of the Choquard equations with a sign-changing self-interaction potential
  • Existence of solutions for a fractional Choquard--type equation in R with critical exponential growth
  • Existence and symmetry of solutions to 2-D Schrödinger-Newton equations
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  • Local existence and uniqueness for the frictional Newton-Schroedinger equation in three dimensions
  • Symmetric Potentials Beget Symmetric Ground States
  • On Rayleigh-Type Formulas for a Non-local Boundary Value Problem Associated with an Integral Operator Commuting with the Laplacian
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