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}
}