We study the existence of ground state solutions for a class of non-linear pseudo-relativistic Schr ̈odinger equations with combined focusing- defocusing nonlinearity of power and Hartree-type. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We apply variational methods to a related elliptic boundary problem on R^{N+1} with a suitable nonlinear Neumann boundary + conditions.
Ground states for pseudo-relativistic equations with combined power and Hartree-type nonlinearities
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 combined focusing- defocusing nonlinearity of power and Hartree-type. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We apply variational methods to a related elliptic boundary problem on R^{N+1} with a suitable nonlinear Neumann boundary + conditions.File in questo prodotto:
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