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SUMMARY:Thomas Bartsch (Universität Gießen)
DTSTART:20200907T130000Z
DTEND:20200907T140000Z
DTSTAMP:20260423T021153Z
UID:SNPDEA/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SNPDEA/3/">N
 ormalized solutions of nonlinear elliptic problems</a>\nby Thomas Bartsch 
 (Universität Gießen) as part of "Partial Differential Equations and Appl
 ications" Webinar\n\n\nAbstract\nThe talk will be concerned with the exist
 ence of $L^2$ normalized solutions to nonlinear elliptic equations and sys
 tems. A model problem is the system of nonlinear Schrödinger equations\n\
 n$$-\\Delta u+\\lambda_1 u = \\mu_1 u^3 + \\beta u v^2 \\qquad \\in \\math
 bb{R}^3$$\n$$-\\Delta v+\\lambda_2 v = \\mu_2 v^3 + \\beta u^2 v \\qquad \
 \in \\mathbb{R}^3$$\n\nwith normalization constraints\n\n$$\\int_{\\mathbb
 {R}^3} u^2 = a^2  \\quad \\text{and}\\quad \\int_{\\mathbb{R}^3} v^2 = b^2
  \\\, .$$\n\nWhereas nonlinear elliptic equations and systems have been in
 vestigated intensively since the 1960s\, in comparison surprisingly little
 \nis known about solutions with prescribed $L^2$ norms. We discuss this\np
 roblem and survey recent results.\nThe talk is based on joint work with Lo
 uis Jeanjean\, Yanyan Liu\,\nZhaoli Liu\, Nicola Soave\, Xuexiu Zhong\, We
 nming Zou.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/3/
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