Acta mathematica scientia, Series B >
BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS
Received date: 2016-08-02
Online published: 2017-04-25
Supported by
Na Ba was supported by National Natural Science Foundation of China (11201132), Scientific Research Foundation for Ph.D of Hubei University of Technology (BSQD12065), and the Scientific Research Project of Education Department of Hubei Province (Q20151401).
We study the bound states to nonlinear Schrödinger equations with electromagnetic fields ih (∂ψ/∂t)=(h/i▽-A(x))2ψ + V(x)ψ-K(x)|ψ|p-1ψ=0, on R+×RN. Let G (x)=[V (x)](p+1)/(p-1)-N/2[K(x)]-2/(p-1) and suppose that G(x) has k local minimum points. For h > 0 small, we find multi-bump bound states ψh(x, t)=e-iEt/h uh(x) with uh concentrating at the local minimum points of G(x) simultaneously as h → 0. The potentials V (x) and K(x) are allowed to be either compactly supported or unbounded at infinity.
Na BA , Jinjun DAI . BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS[J]. Acta mathematica scientia, Series B, 2017 , 37(2) : 405 -424 . DOI: 10.1016/S0252-9602(17)30011-5
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