Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904553 | Acta Mathematica Scientia | 2017 | 20 Pages |
Abstract
We study the bound states to nonlinear Schrödinger equations with electro-magnetic fields
ihâÏât=(hiâ-A(x))2Ï+V(x)Ï-K(x)|p-1Ï=0,onâ+ÃâN. Let
G(x)=[V(x)]p+1p-1-N2[K(x)]-2p-1 and suppose that G(x) has k local minimum points. For h > 0 small, we find multi-bump bound states Ïh(x,t) = eâlEt/hUh(Ï) with Uh concentrating at the local minimum points of G(x) simultaneously as h â 0. The potentials V(x) and K(x) are allowed to be either compactly supported or unbounded at infinity.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Na BA, Jinjun DAI,