Wednesday, March 26, 2025 — 11:30 am — aula M1.6, edificio Matematica
Normalized solutions to NLS equations in dimension two
Abstract: We are concerned with positive mass-normalized solutions to semi-linear Schrödinger equations. We are interested in the so-called mass mixed case in which the nonlinearity has $L^2$-subcritical growth at zero and critical growth at infinity, which in dimension two turns out to be of exponential rate. Under mild conditions, we establish the existence of two positive normalized solutions provided the prescribed mass is sufficiently small: one is a local minimizer and the second one is of mountain pass type. We also investigate the asymptotic behavior of solutions approaching the zero mass case, when the normalization constant vanishes.