Differential and Integral Equations

Infinitely many solutions for a class of sublinear Schrödinger-Maxwell equations in $\mathbb{R}^{N}$ with indefinite weight functions

Anouar Bahrouni and Hichem Ounaies

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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.

Article information

Source
Differential Integral Equations, Volume 27, Number 1/2 (2014), 45-57.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1384282853

Mathematical Reviews number (MathSciNet)
MR3161595

Zentralblatt MATH identifier
1313.35078

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35B38: Critical points

Citation

Bahrouni, Anouar; Ounaies, Hichem. Infinitely many solutions for a class of sublinear Schrödinger-Maxwell equations in $\mathbb{R}^{N}$ with indefinite weight functions. Differential Integral Equations 27 (2014), no. 1/2, 45--57. https://projecteuclid.org/euclid.die/1384282853


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