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UID:news616@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190119T205412
DTSTART;TZID=Europe/Zurich:20140411T160000
SUMMARY:BZ Seminar in Analysis: Tobias Weth (Frankfurt)
DESCRIPTION:Unlike in the case of nonlinear stationary Schršdinger equatio
 ns\, the  existence of standing wave solutions to nonlinear Helmholtz equa
 tions is  relatively unexplored up to now since the linearized problem lac
 ks the  Fredholm property in standard Sobolev spaces. I will present a dua
 l  variational approach to detect real-valued standing wave solutions in  
 the case of power type nonlinearities of the form $Q(x)|u|^{p-2}u$. Via  t
 his approach\, existence results will be derived for a periodic weight  fu
 nction $Q$ and in the case where $Q$ decays to zero asymptotically in  spa
 ce. In the periodic case\, a key ingredient of the method is a new  nonvan
 ishing result related to an associated integral equation. I will  also dis
 cuss the far field asymptotics of the solutions obtained by this  approach
 .  This is joint work with Gilles Evequoz (University of Frankfurt).
X-ALT-DESC: Unlike in the case of nonlinear stationary Schršdinger equatio
 ns\, the  existence of standing wave solutions to nonlinear Helmholtz equa
 tions is  relatively unexplored up to now since the linearized problem lac
 ks the  Fredholm property in standard Sobolev spaces. I will present a dua
 l  variational approach to detect real-valued standing wave solutions in  
 the case of power type nonlinearities of the form $Q(x)|u|^{p-2}u$. Via  t
 his approach\, existence results will be derived for a periodic weight  fu
 nction $Q$ and in the case where $Q$ decays to zero asymptotically in  spa
 ce. In the periodic case\, a key ingredient of the method is a new  nonvan
 ishing result related to an associated integral equation. I will  also dis
 cuss the far field asymptotics of the solutions obtained by this  approach
 .  This is joint work with Gilles Evequoz (University of Frankfurt). 
DTEND;TZID=Europe/Zurich:20140411T170000
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