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SUMMARY:An action approach to nodal and least energy normalized solutions 
 for nonlinear Schrödinger equations
DTSTART:20250625T120000Z
DTEND:20250625T130000Z
DTSTAMP:20260423T142900Z
UID:indico-event-14522@indico.math.cnrs.fr
DESCRIPTION:Speakers: Damien Galant\n\nIn this talk\, I will present two n
 otions of stationary state solutions to the nonlinear Schrödinger equatio
 n:\nthose with a fixed frequency\, corresponding to critical points of the
  action functional\,\nand those with fixed mass (normalized solutions)\, c
 orresponding to critical points\nof the energy functional constrained on a
  L²-sphere.\nIn general\, it is somewhat easier to treat the problem with
  a fixed frequency.\nIn particular\, in this case one is able to find leas
 t action solutions\nand least action nodal solutions for all Sobolev-subcr
 itical exponents in the nonlinearity.\nRegarding the fixed mass solutions\
 , a new critical exponent appears.\nFinding normalized solutions in the "m
 ass-supercritical" regime is usually a difficult problem\,\nexplored since
  pioneering work by Jeanjean in the late 1990s and often imposing geometri
 cal conditions\non the domain on which the equation is set. We will presen
 t a new method which allows\nto characterize the masses of the least actio
 n solutions and the least action normalized solutions\,\ntherefore buildin
 g a bridge between the study of solutions having a fixed frequency and tho
 se having a fixed mass.\nAs we will see\, we will do so in a new "variatio
 nal" fashion since one does not expect in general\nto have continuous bran
 ches of solutions for all values of the frequency.\nThis is joint work wit
 h Colette De Coster (CERAMATHS/DMATHS\, UPHF and INSA HdF\, Valenciennes\,
  France)\,\nSimone Dovetta (Politecnico di Torino\, Italy) and Enrico Serr
 a (Politecnico di Torino).\n\nhttps://indico.math.cnrs.fr/event/14522/
LOCATION:Salle Huron (1R1-106)
URL:https://indico.math.cnrs.fr/event/14522/
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