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SUMMARY:On a nonlinear Schrödinger equation: uniqueness\, non-degeneracy 
 and applications
DTSTART:20210319T141500
DTSTAMP:20260413T152847Z
UID:b580726ca61ae8a2772657a7286000f318408d5b3854151bc3697a94
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Simona Rota Nodari\, Institut de Mathématiques de Bourgog
 ne\n\nAbstract: In this talk\, I will first state a general result about t
 he uniqueness and the non-degeneracy of positive radial solutions to some 
 semi-linear elliptic equations $-\\Delta u=g(u)$. Then I will consider the
  case of the double power non-linearity $g(u)=u^q-u^p-\\mu u$ for $p>q>1$ 
 and $\\mu>0$. In this case\, the non-degeneracy of the unique solution $u_
 \\mu$ allows us to derive its behavior in the two limits $\\mu \\to 0$ and
  $\\mu\\to\\mu_*$ where $\\mu_*$ is the threshold of existence. This impli
 es the uniqueness of energy minimizers at fixed mass in certain regimes. M
 oreover\, for $\\mu$ close to $\\mu_*$\, this gives some important informa
 tion about the orbital stability of $u_\\mu$ and allows us to provide a ma
 thematical explanation for the occurence of a 'saturation phenomenon' whic
 h plays an important role in Physics.\n\n\n\n\n\n \n \n\n\n\n\n\n\n
LOCATION:https://epfl.zoom.us/j/84427796396
STATUS:CONFIRMED
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