Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges

  • Phan Thành Nam
  • Hanne Van Den BoschEmail author


We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.


Thomas-Fermi-Dirac-von Weizsäcker Theory Ionization problem Concentration-compactness method 

Mathematics Subject Classification (2010)



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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria
  2. 2.Instituto de FísicaPontificia Universidad Católica de ChileSantiagoChile

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