General Theorem on Bifurcation and Its Application to the Hartree Equation of the Helium Atom
- 1 August 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (8) , 2505-2512
- https://doi.org/10.1063/1.1665418
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.This publication has 2 references indexed in Scilit:
- On positive eigenvalues of one‐body schrödinger operatorsCommunications on Pure and Applied Mathematics, 1969
- Estimation of the bifurcation coefficient for nonlinear eigenvalue problemsZeitschrift für angewandte Mathematik und Physik, 1969