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Comptes Rendus Mathématique
Volume 354, n° 1
pages 75-80 (janvier 2016)
Doi : 10.1016/j.crma.2015.10.018
Received : 25 October 2014 ;  accepted : 23 October 2015
Multiplicity for a 4-sublinear Schrödinger–Poisson system with sign-changing potential via Morse theory

Hongliang Liu a , Haibo Chen a , Gangwei Wang b, c
a School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China 
b Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada 
c School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China 


In this paper, we study a 4-sublinear Schrödinger–Poisson system with sign-changing potential. Under some suitable assumptions, the existence of two nontrivial solutions are obtained by using the Morse theory. Our result improves the recent ones of Chen and Zhang (2014) [[6]].

The full text of this article is available in PDF format.

Keywords : Schrödinger–Poisson system, Morse theory, Critical groups, Sign-changing potential

 Research supported by Hunan Provincial Foundation For Postgraduate CX2014B044, National Natural Science Foundation of China 11271372 and Hunan Provincial Natural Science Foundation of China 12JJ2004.

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