Bifurcation and regularity analysis of the Schrödinger-Poisson equation

Abstract

Abstract The aim of this paper is to present bifurcation results for (weak) solutions of the Schrödinger-Poisson system in R 3 , involving subcritical and critical nonlinearities and using the global bifurcation theorem. Furthermore, we establish the existence of unbounded components of (weak) solutions, which bifurcate from trivial solutions and from infinity, respectively. The novelties of the paper lie in the appearance of the indefinite nonlinearity and the critical nonlinear term. Finally, we also analyze the regularity result that guarantees the L ∞ -bound of the (weak) solutions of the nonlinear Schrödinger-Poisson system under consideration.