Boundary concentration of a Gauged nonlinear Schrödinger equation on large balls

By Alessio Pomponio, D. Ruiz. 2013

76 citations recorded by the source corpus.

This paper is motivated by a gauged Schrödinger 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.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7cb027787f3a118a2fc9ca3a94093b7c16b12264

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In Applied Mathematics

1. Xiaoyutao Luo
2. Gongbao Li
3. Nikolaos S. Papageorgiou
4. Hongyu Ye
5. Giovany M. Figueiredo

In Control and Systems Engineering

1. Xiaoyutao Luo
2. Gongbao Li
3. Hongyu Ye

In Mathematical Physics

1. Xiaoyutao Luo
2. Gongbao Li
3. Xianhua Tang
4. Hongyu Ye

Citations in the corpus

• Normalized solutions for the Chern–Simons–Schrödinger equation in R^2 (2017, background): “They also studied in [30] the bounded domain case for p ∈ (2, 4).”