Milan Journal of Mathematics

, Volume 76, Issue 1, pp 257–274

On Schrödinger-Poisson Systems

Article

DOI: 10.1007/s00032-008-0094-z

Cite this article as:
Ambrosetti, A. Milan j. math. (2008) 76: 257. doi:10.1007/s00032-008-0094-z

Abstract.

We discuss some recent results dealing with the existence of bound states of the nonlinear Schrödinger-Poisson system
$$\left\{ \begin{gathered} - \Delta u + V(x)u + \lambda K(x)\phi (x)u = |u|^{{p - 1}} u, \hfill \\ - \Delta \phi = K(x)u^{2}, \hfill \\ \end{gathered} \right.$$
as well as of the corresponding semiclassical limits. The proofs are based upon Critical Point theory and Perturbation Methods.

Mathematics Subject Classification (2000).

Primary 35J10Secondary 35J20, 35J60, 35Q55

Keywords.

Schrödinger-Poisson equationVariational methodsPerturbation methods

Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  1. 1.SISSATriesteItaly