Concentration of semi-classical solutions to the Chern–Simons–Schrödinger systems

Abstract

In this paper we demonstrate the existence and concentration behavior of semi-classical solutions for the nonlinear Chern–Simons–Schrödinger systems with external potential. Combining the variational methods with concentration compactness principle, we prove the existence of a family of semi-classical solutions concentrating at the minimum points of the external potential.

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Correspondence to Jinggang Tan.

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Wan, Y., Tan, J. Concentration of semi-classical solutions to the Chern–Simons–Schrödinger systems. Nonlinear Differ. Equ. Appl. 24, 28 (2017). https://doi.org/10.1007/s00030-017-0448-8

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Keywords

  • Chern–Simons gauge field
  • Schrödinger equation
  • Variational methods
  • Concentration

Mathematics Subject Classification

  • 35J50
  • 35J10