Applied Analysis

Seminar information archive ~07/17Next seminarFuture seminars 07/18~

Date, time & place Thursday 16:00 - 17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

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16:00-17:30   Room #118 (Graduate School of Math. Sci. Bldg.)
Norihisa Ikoma (Keio University)
Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent
[ Abstract ]
This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).