Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms
Volume 11, Issue 5, pp 591--601
http://dx.doi.org/10.22436/jnsa.011.05.01
Publication Date: March 25, 2018
Submission Date: January 29, 2017
Revision Date: November 22, 2017
Accteptance Date: January 11, 2018
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Authors
Da-Bin Wang
- Department of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People’s Republic of China.
Lu-Ping Ma
- Department of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People’s Republic of China.
Wen Guan
- Department of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People’s Republic of China.
Hong-Mei Wu
- Department of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People’s Republic of China.
Abstract
In this paper, we consider the following nonlinear Schrödinger-Poisson system
\[
\left\{
\renewcommand{\arraystretch}{1.25}
\begin{array}{ll}
-\Delta u + V(x)u+K(x)\phi u= f(x,u), x\in \mathbb{R}^3,\\
-\Delta \phi=K(x)u^{2}, x\in \mathbb{R}^3,
\end{array}
\right.
\]
where~\(V, K\in L^{\infty}(\mathbb{R}^3)\) and \(f:\mathbb{R}^3\times\mathbb{R}\rightarrow\mathbb{R}\) is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of \(V, K\), and \(f\) at infinity. Moreover, the nonlinear term \(f\) does not satisfy any monotone condition.
Share and Cite
ISRP Style
Da-Bin Wang, Lu-Ping Ma, Wen Guan, Hong-Mei Wu, Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 591--601
AMA Style
Wang Da-Bin, Ma Lu-Ping, Guan Wen, Wu Hong-Mei, Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms. J. Nonlinear Sci. Appl. (2018); 11(5):591--601
Chicago/Turabian Style
Wang, Da-Bin, Ma, Lu-Ping, Guan, Wen, Wu, Hong-Mei. "Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 591--601
Keywords
- Schrödinger-Poisson system
- asymptotically periodic
- variational method
MSC
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