Revista Matemática Iberoamericana
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Published online: 2013-12-15
Ground states for pseudo-relativistic Hartree equations of critical typeVittorio Coti Zelati and Margherita Nolasco (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. Iberoam. 29 (2013), 1421-1436. doi: 10.4171/RMI/763