We study existence and regularity of positive stationary solutions for a class of nonlinear pseudo-relativistic Schrödinger 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.
Cite this article
Vittorio Coti Zelati, Margherita Nolasco, Existence of ground states for nonlinear, pseudo-relativistic Schrödinger equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 1, pp. 51–72DOI 10.4171/RLM/587