Taiwanese Journal of Mathematics

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS

Zhisu Liu, Shangjiang Guo, and Ziheng Zhang

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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


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