典型文献
A NONLINEAR SCHRODINGER EQUATION WITH COULOMB POTENTIAL
文献摘要：
In this paper,we study the Cauchy problem for the nonlinear Schr?dinger equa-tions with Coulomb potential i?tu+Δu+K/|x|u=λ|u|p-1u with 1＜p≤5 on R3.Our results reveal the influence of the long range potential K|x|-1 on the existence and scattering theories for nonlinear Schr?dinger equations.In particular,we prove the global existence when the Coulomb potential is attractive,i.e.,when K＞0,and the scattering theory when the Coulomb potential is repulsive,i.e.,when K≤0.The argument is based on the newly-established interaction Morawetz-type inequalities and the equivalence of Sobolev norms for the Laplacian operator with the Coulomb potential.
文献关键词：
中图分类号：
作者姓名：
Changxing MIAO;Junyong ZHANG;Jiqiang ZHENG
作者机构：
Institute of Applied Physics and Computational Mathematics,Beijing 100088,China;Department of Mathematics,Beijing Institute of Technology,Beijing 100081,China;Department of Mathematics,Cardiff University,UK
文献出处：
引用格式：
[1]Changxing MIAO;Junyong ZHANG;Jiqiang ZHENG-.A NONLINEAR SCHRODINGER EQUATION WITH COULOMB POTENTIAL)[J].数学物理学报（英文版）,2022(06):2230-2256
A类：
NONLINEAR,SCHRODINGER,EQUATION,COULOMB,POTENTIAL,tu+,u+K,Morawetz
B类：
WITH,In,this,paper,study,Cauchy,problem,nonlinear,Schr,dinger,Coulomb,potential,1u,R3,Our,results,reveal,influence,long,range,existence,scattering,theories,equations,particular,prove,global,when,attractive,theory,repulsive,argument,newly,established,interaction,type,inequalities,equivalence,Sobolev,norms,Laplacian,operator
AB值：
0.458247
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