质量临界情形下一类具平方反比势的非齐次非线性Schrödinger方程  

A Masscritical Inhomogeneous Nonlinear Schrödinger Equation with Inversesquare Potential

作　　者：李玉林 黄娟 LI Yulin;HUANG Juan(College of General Education,City College of Southwest University of Science and Technology,Mianyang 621000,Sichuan;V.C.&V.R.Key Lab,Sichuan Normal University,Chengdu 610066,Sichuan;School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]西南科技大学城市学院通识教育学院,四川绵阳621000 [2]可视化计算与虚拟现实四川省重点实验室,四川成都610066 [3]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2021年第6期762-766,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11401409);四川省科技厅应用基础研究项目(2018JY0486)

摘　　要：讨论一类具有平方反比势的质量临界非齐次非线性Schrödinger方程,通过研究该方程对应稳态方程的变分结构得到驻波解的存在性,进而建立整体解存在的门槛条件.通过伪共形变换和基态解构造出方程具正能量的爆破解,进一步得到驻波的强不稳定性.In this paper,we study a mass-critical inhomogeneous nonlinear Schrödinger equation with inverse-square potential. By analyzing the variational structure of the corresponding stationary equation,the existence of the standing waves is obtained,and then the sharp threshold for the global existence is given. By applying the pseudoconformal transformation law,a blowup solution of the equation with positive energy is constructed by the ground state solution,which implies the standing waves are strongly unstable.

关 键 词：质量临界 驻波解 强不稳定性 

分 类 号：Q175.29[生物学—水生生物学]