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Author: Fall, Mouhamed Moustapha × Type: Text ×

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    Ground states and concentration phenomena for the fractional Schrödinger equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Fall, Mouhamed Moustapha; Mahmoudi, Fethi; Valdinoci, Enrico
    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.
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    Uniqueness and nondegeneracy of positive solutions of (-Delta) su + u = up in RN when s is close to 1
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Fall, Mouhamed Moustapha; Valdinoci, Enrico
    We consider the equation (-Δ)s u+u = up with s ∈ (0,1) in the subcritical range of p. We prove that if s is sufficiently close to 1 the equation possesses a unique minimizer, which is nondegenerate.