Multiple normalized solutions of Chern–Simons–Schrödinger system

  • Jianjun YuanEmail author


In this paper, we consider the following equation
$$-\Delta u + \omega u + \left(\int_{|x|}^{\infty}\frac{h(s)}{s}u^2(s)ds\right) u + \frac{h^2(|x|)}{|x|^2}u - \lambda|u|^{p - 2}u = 0\quad \mbox{in}\quad \mathbb{R}^2,$$
for p >  2 and \({\lambda > 0}\) , which appeared in Byeon et al. (J Funct Anal 263(6):1575–1608, 2012) to find the standing wave solutions of the Chern–Simons–Schrödinger system. By using the minimax theorem, we get the multiplicity results for the L 2-normalized solutions to the equation, and thus there are multiple L 2-normalized solutions of the Chern–Simons–Schrödinger system.


Palais–Smale sequence Euler–Lagrange equation Pohozaev identity Standing wave 

Mathematics Subject Classification

35Q55 35A15 35B30 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.The College of Information and TechnologyNanjing University of Chinese MedicineNanjingChina

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