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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Infinitely many solutions for a Schrödinger-Poisson system with concave and convex nonlinearities

Pages: 427 - 440, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.427

 
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Mingzheng Sun - School of Mathematical Sciences, Capital Normal University, Beijing 100037, China (email)
Jiabao Su - School of Mathematical Sciences, Capital Normal University, Beijing 100037, China (email)
Leiga Zhao - Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China (email)

Abstract: In this paper, we obtain the existence of infinitely many solutions for the following Schrödinger-Poisson system \begin{equation*} \begin{cases} -\Delta u+a(x)u+ \phi u=k(x)|u|^{q-2}u- h(x)|u|^{p-2}u,\quad &x\in \mathbb{R}^3,\\ -\Delta \phi=u^2,\ \lim_{|x|\to +\infty}\phi(x)=0, &x\in \mathbb{R}^3, \end{cases} \end{equation*} where $1 < q < 2 < p < +\infty$, $a(x)$, $k(x)$ and $h(x)$ are measurable functions satisfying suitable assumptions.

Keywords:  Schrödinger-Poisson system, infinitely many solutions, concave and convex nonlinearities, nonlocal term, variational methods.
Mathematics Subject Classification:  35J60, 35Q35.

Received: November 2013;      Revised: March 2014;      Available Online: August 2014.

 References