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January/February 2014 Infinitely many solutions for a class of sublinear Schrödinger-Maxwell equations in $\mathbb{R}^{N}$ with indefinite weight functions
Anouar Bahrouni, Hichem Ounaies
Differential Integral Equations 27(1/2): 45-57 (January/February 2014).

Abstract

This paper considers the following sublinear Schrödinger-Maxwell system \begin{equation}\label{man} \begin{cases} -\Delta u+V(x)u+K(x) \phi u =a(x) |u |^{q-1}u, \ \ \ \ \ \mbox{in} \ \ \mathbb{R}^{N},\\ -\Delta \phi = K(x)u^{2}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mbox{in} \ \ \mathbb{R}^{N}, \end{cases} \end{equation} where $N=3, $ $ 0 <q <1,$ and $ a,K,V\in{L^{\infty}} (\mathbb{R}^{3} )$. We suppose that $K$ is a positive function and $a, V$ both change sign in $\mathbb{R}^{3}$. There seems to be no results on the existence of infinitely many solutions to problem (0.1). The proof is based on the Symmetric Mountain Pass theorem.

Citation

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Anouar Bahrouni. Hichem Ounaies. "Infinitely many solutions for a class of sublinear Schrödinger-Maxwell equations in $\mathbb{R}^{N}$ with indefinite weight functions." Differential Integral Equations 27 (1/2) 45 - 57, January/February 2014.

Information

Published: January/February 2014
First available in Project Euclid: 12 November 2013

zbMATH: 1313.35078
MathSciNet: MR3161595

Subjects:
Primary: 35B38, 35J20

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 1/2 • January/February 2014
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