Normalized solutions for Schr¨odinger equations with mixed power nonlinearities

Thời gian: 20h ngày 28 tháng 10 năm 2025
Hình thức: Online

Tóm tắt: From the physical point of view, since, in addition to being a conserved quantity for time-dependent nonlinear Schr¨odinger equations, the mass often has a clear physical meaning; for instance, it represents the power supply in nonlinear optics, condensed matter physics or plasma physics, etc, we focus on studying solutions having prescribed mass, namely normalized solutions. Therefore, we are interested in looking for normalized solutions to time-independent nonlinear Schr¨odinger equations with mixed power nonlinearities. The existence, multiplicity, and stability issues of normalized solutions are considered with both Sobolev sub-critical and Sobolev critical cases. Since normalized solutions are found as critical points of an associated functional on a constraint, the main ingredients of the proofs are variational methods. The content of the talk is based on works of [Soave - JDE (2020)], [Soave - JFA (2020)], [Jeanjean & Jendrej & Le & Visciglia (2022)], [Jeanjean & Le (2022)] and [Wei & Wu (2022)].