Existence of small positive solutions to the nonlinear Schrödinger equation

Prof. Norihisa Ikoma (Keio University, Tokyo)
Existence of small positive solutions to the nonlinear Schrödinger equation

Abstract
This talk is concerned with the existence of positive solutions to the nonlinear Schrödinger equation. One of the features is a coefficient of the nonlinearity which we regard as a parameter. Under some conditions on the nonlinearity around 0, we show the existence of positive solutions when the parameter (the coefficient of the nonlinearity) is sufficiently large. We also seek for the asymptotic behavior of positive solutions when the parameter diverges to the infinity. This is joint work with Shinji Adachi (Shizuoka University) and Tatsuya Watanabe (Kyoto Sangyo University).