## On the existence of solutions for Schrödinger-Maxwell systems in $$R^3$$.(English)Zbl 1253.35166

Summary: In this paper we discuss the existence of solutions for the following Schrödinger-Maxwell systems $\begin{cases} -\Delta\psi+\lambda\psi+b(x)\phi\psi=a(x)|\psi|^{p-1}\psi \quad & \text{in} \, \mathbb R^3,\\ -\Delta\psi=4\pi b(x)\psi^2 \quad & \text{in} \, \mathbb R^3. \end{cases}$ Under suitable assumptions on $$a(x)$$ and $$b(x)$$, we establish existence results by variational methods.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35Q61 Maxwell equations 35J20 Variational methods for second-order elliptic equations 35J60 Nonlinear elliptic equations
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