Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616851 | Journal of Mathematical Analysis and Applications | 2013 | 15 Pages |
Abstract
We study the existence and multiplicity of solutions of the following nonlinear Schrödinger equation in the presence of magnetic field: {(−iε∇+A(x))2u+V(x)u=(K(x)∗|u|p)|u|p−2u,|u|∈H1(RN) where V:RN→RV:RN→R is the external potential, K:RN→RK:RN→R is the response function and A=(A1,…,AN):RN→RNA=(A1,…,AN):RN→RN is the magnetic vector potential associated to an external magnetic field BB, that is B=curlAB=curlA. Under suitable assumptions on the functions V(x),K(x)V(x),K(x) and A(x)A(x), if the parameter εε is small enough, we can prove the multiplicity of bound states for the equation by variational methods.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Minbo Yang, Yuanhong Wei,