## Differential and Integral Equations

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

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

Anouar Bahrouni and Hichem Ounaies

#### 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