Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 37, pp. 1-18.

Title: Multiple semiclassical states for singular magnetic
       nonlinear Schrodinger equations
 
Author: Sara Barile (Politecnico di Bari, Italy)

Abstract: 
 By means of a finite-dimensional reduction, we show
 a multiplicity result of semiclassical solutions
 $u: \mathbb{R}^N \to\mathbb{C}$
 to the singular nonlinear Schrodinger equation
 $$
 \Big( \frac{\varepsilon}{i} \nabla -  A(x)\Big)^2 u +
 u+(V(x)-\gamma(\varepsilon)W(x)) u = K(x) | u|^{p-1} u, \quad x \in
 \mathbb{R}^N,
 $$
 where $N \geq 2$, $1 < p < 2^{*}-1$, $A(x), V(x)$ and $K(x)$
 are bounded potentials. Such solutions concentrate  near
 (non-degenerate) local extrema or  a
 (non-degenerate) manifold of stationary points of an
 auxiliary function $\Lambda$ related to the unperturbed electric
 field $V(x)$ and the coefficient $K(x)$ of the nonlinear term.
 
Submitted November 26, 2007. Published March 14, 2008.
Math Subject Classifications: 35J10, 35J60, 35J20, 35Q55, 58E05.
Key Words: Nonlinear Schrodinger equations; external magnetic field; 
           singular potentials; semiclassical limit.