Seminars

Uniqueness of standing waves for nonlinear Schrodinger equations

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Yoshihito Oshita

2007-10-18
15:00:00 - 16:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

For $m > 0$ and $ p \\in (1,(N+2)/(N-2)),$ we show the uniqueness and a linearized non-degeneracy of solutions for the following problem \\[ \\Delta u - |x|^mu + u^p = 0, \\quad u > 0\\textrm{ in } \\mathbf{R}^N \\textrm{ and } \\lim_{|x| \\to \\infty}u(x) = 0.\\]