Uniqueness and non-degeneracy for a class of semilinear elliptic equations

Simona Rota_Nodari
Institut de Mathématiques de Bourgogne, Université de Bourgogne, UFR Sciences et Techniques, Faculté des Sciences Mirande, 9 avenue Alain Savary, 21078 Dijon Cedex, France

In this talk, I will present a result on the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Next, I will illustrate this result with two examples: a nonlinear Schrödinger equation for a nucleon and a Schrödinger equation with a double power non-linearity. This talk is based on joint works with Mathieu Lewin.