2013/07/30 by Alessio Pomponio, David Ruiz, Pomponio, Alessio +1 · 1 citation
Mathematics · #35J20 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J20 #msc:35Q55
paper · pdf · doi:10.48550/arxiv.1307.8015
23 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1306.2051
arxiv created 2013/07/30 · arxiv updated 2013/07/31
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.