Ground states for pseudo-relativistic Hartree equations of critical type

Details Ground states for pseudo-relativistic Hartree equations of critical type Ground states for pseudo-relativistic Hartree equations of critical type

2012-02-11

arxiv.org/abs/1202.2446v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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