Boundary concentration of a Gauged Nonlinear Schrodinger Equation
Analysis of PDEs
2013-07-31 v1
Abstract
This paper is motivated by a gauged Schrodinger equation in dimension 2 including the so-called Chern-Simons term. The radially symmetric case leads to an elliptic problem with a nonlocal defocusing term, in competition with a local focusing nonlinearity. In this work we pose the equations in a ball under homogeneous Dirichlet boundary conditions. By using singular perturbation arguments we prove existence of solutions for large values of the radius. Those solutions are located close to the boundary and the limit profile is given.
Keywords
Cite
@article{arxiv.1307.8015,
title = {Boundary concentration of a Gauged Nonlinear Schrodinger Equation},
author = {Alessio Pomponio and David Ruiz},
journal= {arXiv preprint arXiv:1307.8015},
year = {2013}
}
Comments
23 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1306.2051