Revista Matemática Iberoamericana


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Volume 29, Issue 4, 2013, pp. 1421–1436
DOI: 10.4171/RMI/763

Published online: 2013-12-15

Ground states for pseudo-relativistic Hartree equations of critical type

Vittorio Coti Zelati[1] and Margherita Nolasco[2]

(1) Università degli Studi di Napoli Federico II, Italy
(2) Università degli Studi dell'Aquila, Italy

We study the existence of ground state solutions for a class of nonlinear pseudo-relativistic Schrödinger 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 this problem using variational methods after transforming the problem to an elliptic equation with a nonlinear Neumann boundary conditions.

Keywords: Nonlinear Schrödinger equation, pseudo-relativistic Hartree approximation, solitary waves, ground states

Coti Zelati Vittorio, Nolasco Margherita: Ground states for pseudo-relativistic Hartree equations of critical type. Rev. Mat. Iberoamericana 29 (2013), 1421-1436. doi: 10.4171/RMI/763