## Differential and Integral Equations

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

#### Abstract

This paper considers the following sublinear Schrödinger-Maxwell system $$\label{man} \begin{cases} -\Delta u+V(x)u+K(x) \phi u =a(x) |u |^{q-1}u, \ \ \ \ \ \mbox{in} \ \ \mathbb{R}^{N},\\ -\Delta \phi = K(x)u^{2}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mbox{in} \ \ \mathbb{R}^{N}, \end{cases}$$ 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

https://projecteuclid.org/euclid.die/1384282853

Mathematical Reviews number (MathSciNet)
MR3161595

Zentralblatt MATH identifier
1313.35078

#### 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