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arXiv · 1202.2446

Ground states for pseudo-relativistic Hartree equations of critical type

Vittorio Coti Zelati·Margherita Nolasco
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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.

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Vittorio Coti Zelati, Margherita Nolasco. 2012-02-11. Ground states for pseudo-relativistic Hartree equations of critical type. https://arxiv.org/abs/1202.2446

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