WIAS Preprint No. 2031, (2014)

Ground states and concentration phenomena for the fractional Schrödinger equation


  • Fall, Mouhamed Moustapha
  • Mahmoudi, Fethi
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35Q55 35R11 35B44 35B40 35J65 35J75


  • Fractional Laplacian, ground states, concentration phenomena, uniqueness




We consider here solutions of the nonlinear fractional Schrödinger equation. We show that concentration points must be critical points for the potential. We also prove that, if the potential is coercive and has a unique global minimum, then ground states concentrate suitably at such minimal point. In addition, if the potential is radial, then the minimizer is unique.

Appeared in

  • Nonlinearity, 28 (2015) pp. 1937--1961.

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