Journal
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI
Volume 22, Issue 1, Pages 51-72Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/RLM/587
Keywords
Nonlinear Schrodinger equation; solitary waves; pseudo-relativistic Hartree approximation
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We study existence and regularity of positive stationary solutions for a class of nonlinear pseudo-relativistic Schrodinger equations. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We investigate such problems using critical point theory after transforming them to elliptic equations with nonlinear Neumann boundary conditions.
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