EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS

Abstract

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.