Normalized solution for Schrödinger equation with critical growth in RN

Prof. Claudianor Alves

Date: 18th February 1:30 pm - 2:15 pm (UTC -3) Link: PPGM/UFSCar Youtube channel

Abstract: In this lecture I will talk about the existence of normalized solutions to the following nonlinear Schrödinger equation with critical growth

Claudianor's problem

where a > 0, λ < 0 and f has an exponential critical growth when N = 2, and f(t) = μ|u|q−2u+|u|2∗−2u with q∈(2+4/N ,2), μ > 0 and 2*=2N/N−2 when N ≥ 3. Our main results complement some recent results for N≥3 and it is totally new for N=2. This is a joint work with Olimpio Miyagaki and Chao Ji.