English

Ground states for pseudo-relativistic Hartree equations of critical type

Analysis of PDEs 2012-02-14 v1

Abstract

We study the existence of ground state solutions for a class of non-linear pseudo-relativistic Schr\"odinger equations with critical two-body interactions. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We investigate such a problem using variational methods after transforming the problem to an elliptic equation with a nonlinear Neumann boundary conditions.

Keywords

Cite

@article{arxiv.1202.2446,
  title  = {Ground states for pseudo-relativistic Hartree equations of critical type},
  author = {Vittorio Coti Zelati and Margherita Nolasco},
  journal= {arXiv preprint arXiv:1202.2446},
  year   = {2012}
}