Morse index for solutions of the nonlinear Schrödinger equation in a degenerate setting

In this paper, we study the Morse index of the single-peak solutions concentrating at a point P∊ ℝN of the problem where ε is a positive parameter, if N ≥ 3, p1 if N = 2 and V∊ C∞(ℝN) satisfies 0 < V0≤ V(x)≤ V1. The point P is a critical point of V (possibly degenerate). We will also consider som...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2007-07, Vol.186 (3), p.433-453
Main Authors: Grossi, Massimo, Servadei, Raffaella
Format: Article
Language:English
Subjects:
Critical point
Schrodinger equation
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Summary:In this paper, we study the Morse index of the single-peak solutions concentrating at a point P∊ ℝN of the problem where ε is a positive parameter, if N ≥ 3, p1 if N = 2 and V∊ C∞(ℝN) satisfies 0 < V0≤ V(x)≤ V1. The point P is a critical point of V (possibly degenerate). We will also consider some ‘strong degeneracy’ of P like the case where P belongs to a flat region of maxima.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-006-0013-2