Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential

• Autoři: MUKHERJEE Debangana; NAM Phan Thanh; NGUYEN Phuoc Tai
• Rok publikování: 2021
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Journal of Functional Analysis
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1016/j.jfa.2021.109092
• Doi: http://dx.doi.org/10.1016/j.jfa.2021.109092
• Klíčová slova: Nonlinear Schrodinger equation; Inverse square potential; Hardy-Gagliardo-Nirenberg inequality; Ground state solutions
• Popis: We consider the focusing nonlinear Schrodinger equation with the critical inverse square potential. We give the first proof of the uniqueness of the ground state solution. Consequently, we obtain a sharp Hardy-Gagliardo-Nirenberg interpolation inequality. Moreover, we provide a complete characterization for the minimal mass blow-up solutions to the time dependent problem.

Související projekty

• Lineární a nelineární eliptické rovnice se singulárními daty a související problémy