Global bifurcation for nonlinear Dirac problems

Abstract

In this paper we consider the nonlinear eigenvalue problems for the one-dimensional Dirac equation. To exploit oscillatory properties of the components of the eigenvector-functions of linear one-dimensional Dirac system an appropriate family of sets is introduced. We show the existence of two families of continua of solutions contained in these sets and bifurcating from the intervals of the line of trivial solutions.

Keywords

• nonlinear one-dimensional dirac system
• bifurcation point
• eigenvalue
• eigenvector-function
• oscillation properties of the eigenvector-functions