Title: On the Bartsch-Jeanjean-Soave's open problem and a global branch approach to study of the normalized solution problems

Speaker: Zhong Xuexiu(School of Mathematical Sciences, South China Normal University )

Time: 2023/06/21 14:00-15:00 pm  (Chinese Standard Time)

Tencent Meeting ID:  516 607 599   

Abstract: Sirakov's open problem[Comm. Math. Phys., 2007] is focused on the best range of the parameters where the positive solution exists for an Bose-Einstein Condensation system with prescribed frequencies. Parallelly, Bartsch, Jeanjean and Soave [J. Math. Pures  Appl., 2016] proposed an open problem focusing on the best range of the parameters guaranteeing the existence of positive solution for the Bose-Einstein Condensation system with prescribed masses.

    In this talk, I will introduce a global branch approach developed (with Bartsch and Zou) in [Math.  Ann., 2021] and give an answer to Bartsch-Jeanjean-Soave's open problem. In particular,  in the preprint [arXiv:2112.05869], we (with Jeanjean and Zhang) further develop a global branch approach without eigenvalues, and successfully applying it to give a unified way nonlinearies, which are either mass sub-critical, mass critical or mass super-critical, to the study of the normalized solutions for the Schrödinger equation.