A Note on Non-radial Sign-changing Solutions for the Schr?dinger-Poisson Problem in the Semiclassical Limit

摘要

We study a system of equations known as Schr?dinger-Poisson problem proving that the set of sign-changing solutions has a rich structure in the semiclassical limit. Indeed we construct non-radial multi-peak solutions with an arbitrary large number of positive and negative peaks which are displaced in suitable symmetric configurations and Which collapse to the same point as ? → 0. The proof is based on the Lyapunov-Schmidt reduction.