Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 17, Number 3 (2013), 857-872.
EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS
Zhisu Liu, Shangjiang Guo, and Ziheng Zhang
Abstract
In this paper we are concernedwith a class of sublinear Schrödinger-Maxwell equations $$\begin{cases} -\triangle u + V(x)u + \phi u = f(x,u), &\textrm{in $\mathbb{R}^{3}$}, \\ -\triangle \phi = u^{2}, \lim\limits_{|x| \to +\infty} \phi(x) = 0, &\textrm{in $\mathbb{R}^{3}$}, \end{cases}$$ where $V: \mathbb R^3 \rightarrow \mathbb R$ and $f: \mathbb R^3 \times \mathbb R \rightarrow \mathbb R$. Under certain assumptions on $V$ and $f$, some new criteria on theexistence and multiplicity of negative energy solutions for theabove system are established via the genus properties in criticalpoint theory. Recent results from the literature are significantly improved.
Article information
Source
Taiwanese J. Math., Volume 17, Number 3 (2013), 857-872.
Dates
First available in Project Euclid: 10 July 2017
Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705987
Digital Object Identifier
doi:10.11650/tjm.17.2013.2202
Mathematical Reviews number (MathSciNet)
MR3072265
Zentralblatt MATH identifier
1280.35138
Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations 35J60: Nonlinear elliptic equations
Keywords
Schrödinger-Maxwell equations sublinear genus variational methods
Citation
Liu, Zhisu; Guo, Shangjiang; Zhang, Ziheng. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS. Taiwanese J. Math. 17 (2013), no. 3, 857--872. doi:10.11650/tjm.17.2013.2202. https://projecteuclid.org/euclid.twjm/1499705987