S. Breteaux

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math.AP2026

Existence of Solutions for time-dependent fractional Kohn-Sham Equations

SÃ©bastien Breteaux, Michele Fantechi, JÃ©rÃ©my Faupin

We consider time-dependent Kohn-Sham equations in dimension $3$ with a fractional dispersion relation $(1 - I^)^{s}$ , $s \in (0, \frac{3}{2})$ , and a class of interaction terms including, in…

math.AP2024

On the number of bound states for fractional Schr{Ã¶}dinger operators with critical and super-critical exponent

We study the number $N_{< 0} (H_{s})$ of negative eigenvalues, counting multiplicities, of the fractional SchrÃ¶dinger operator $H_{s} = (- I^)^{s} - V (x)$ on $L^{2} (R^{d})$ , for any $d\ge…