General Theorem on Bifurcation and Its Application to the Hartree Equation of the Helium Atom

Abstract

The existence of a globally extended branch of pointwise positive solutions of a class of nonlinear eigenvalue problems is established. The branch bifurcates from the lowest eigenvalue of the associated linearized problem. The general theorem is then applied to the Hartree equation of the helium atom, giving a rigorous proof for the existence of a solution of this equation.