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.
Ground states for pseudo-relativistic Hartree equations of critical type
NOLASCO, MARGHERITA
2013-01-01
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.File in questo prodotto:
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