Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 1125-1140.doi: 10.1007/s10473-022-0318-2

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THE EXISTENCE AND CONCENTRATION OF GROUND STATE SOLUTIONS FOR CHERN-SIMONS-SCHRÖDINGER SYSTEMS WITH A STEEP WELL POTENTIAL

Jinlan TAN, Yongyong LI, Chunlei TANG   

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
  • Received:2020-12-11 Online:2022-06-26 Published:2022-06-24
  • Contact: Chunlei TANG,E-mail:tangcl@swu.edu.cn E-mail:tangcl@swu.edu.cn
  • Supported by:
    The third author was supported by National Natural Science Foundation of China (11971393).

Abstract: In this paper, we investigate a class of nonlinear Chern-Simons-Schrödinger systems with a steep well potential. By using variational methods, the mountain pass theorem and Nehari manifold methods, we prove the existence of a ground state solution for λ > 0 large enough. Furthermore, we verify the asymptotic behavior of ground state solutions as λ → +∞.

Key words: Chern-Simons-Schrödinger system, steep well potential, ground state solution, concentration

CLC Number: 

  • 35A01
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