Taiwanese Journal of Mathematics


Zhisu Liu, Shangjiang Guo, and Ziheng Zhang

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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.

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Taiwanese J. Math., Volume 17, Number 3 (2013), 857-872.

First available in Project Euclid: 10 July 2017

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Primary: 35J20: Variational methods for second-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations 35J60: Nonlinear elliptic equations

Schrödinger-Maxwell equations sublinear genus variational methods


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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