摘要
In this paper,we study the Cauchy problem for the nonlinear Schrodinger equations with Coulomb potential i■_(t)u+△u+k/|x|u=λ/|u|^(p-l)u with 1<p≤5 on R^(3).Our results reveal the influence of the long range potential K|x|^(-1)on the existence and scattering theories for nonlinear Schrodinger 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≤O.The argument is based on the newlyestablished interaction Morawetz-type inequalities and the equivalence of Sobolev norms for the Laplacian operator with the Coulomb potential.
作者
Changxing MIAO
Junyong ZHANG
Jiqiang ZHENG
苗长兴;张军勇;郑继强(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)
基金
The authors were supported by NSFC(12126409,12026407,11831004)
the J.Zheng was also supported by Beijing Natural Science Foundation(1222019)。
