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2013 EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS
Zhisu Liu, Shangjiang Guo, Ziheng Zhang
Taiwanese J. Math. 17(3): 857-872 (2013). DOI: 10.11650/tjm.17.2013.2202

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.

Citation

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Zhisu Liu. Shangjiang Guo. Ziheng Zhang. "EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS." Taiwanese J. Math. 17 (3) 857 - 872, 2013. https://doi.org/10.11650/tjm.17.2013.2202

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1280.35138
MathSciNet: MR3072265
Digital Object Identifier: 10.11650/tjm.17.2013.2202

Subjects:
Primary: 35J20, 35J60, 35J65

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 3 • 2013
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