## On Schrödinger-Poisson systems.(English)Zbl 1181.35257

Summary: We discuss some recent results dealing with the existence of bound states of the nonlinear Schrödinger-Poisson system
$\begin{cases} -\Delta u + V(x)u + \lambda K(x)\varphi (x)u = |u|^{{p - 1}} u, \\ -\Delta \varphi = K(x)u^{2}, \end{cases}$
as well as of the corresponding semiclassical limits. The proofs are based upon critical point theory and perturbation methods.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35J10 Schrödinger operator, Schrödinger equation 35J20 Variational methods for second-order elliptic equations 35J47 Second-order elliptic systems 35B20 Perturbations in context of PDEs
Full Text: