On the Schrödinger-Maxwell system involving sublinear terms

Abstract

In this paper we study the coupled Schrödinger-Maxwell system $$\{\begin{array}{lll}-△u+u+\varphi u=\lambda \alpha (x)f(u)& \mathrm{in}& {\mathbb{R}}^3,\\ -△\varphi =u^2& \mathrm{in}& {\mathbb{R}}^3,\end{array}$$ where $\alpha \in L^{\infty }({\mathbb{R}}^3)\cap L^{6/(5-q)}({\mathbb{R}}^3)$ for some $q\in (0,1)$, and the continuous function $f:\mathbb{R}\to \mathbb{R}$ is superlinear at zero and sublinear at infinity, e.g., $f(s)=\min (|s{|}^r,|s{|}^p)$ with $0<r<1<p.$ Depending on the range of $\lambda >0$, non-existence and multiplicity results are obtained.

References in corpus (1)

• Multiple critical points for a class of nonlinear functionals

Cited by in corpus (2)

• Regularizing effect for some p-Laplacian systems
• Schrödinger-Maxwell systems on Hadamard manifolds