题    目：Nonlinear Schrödinger equations with competing inhomogeneous nonlinearities: Ground states, Blow-up and Scattering

报告人：缑天祥  副教授

单    位：西安交通大学

时    间：2025年9月19日15:00-17:00

腾讯ID：841-781-002

摘    要：In this talk, we are concerned with solutions to a class of nonlinear Schrödinger equations with competing inhomogeneous nonlinearities. First, we establish the existence/nonexistence, symmetry, decay, uniqueness, non-degeneracy and instability of ground states. Then, we prove scattering versus blow-up below the ground state energy threshold and we also obtain an upper bound of blow-up rate. The novelty here is that the equations under the consideration do not enjoy any scaling invariance due to the presence of competing nonlinearities and the singular weights prevent the invariance by translations in the space variable.

简    介：缑天祥，西安交通大学数学与统计学院副教授，博士毕业于兰州大学，随后在中国科学院数学与系统研究院从事博士后研究工作. 目前, 主要关注非线性薛定谔方程驻波解的存在性及其动力学行为，相关研究成果发表于 J. Funct. Anal., Trans. Amer. Math. Soc., Int. Math. Res. Not. IMRN, Calc. Var. Partial Differential Equations等国际期刊, 曾主持青年科学基金项目一项和博士后科学基金两项, 现主持面上项目一项.