The Nonlinear Perturbation Of Two Linear Eigenvalue Problem

In this paper, there are two nonlinear eigenvalue problem being under consideration: one is about perturbed Dirac operator, and the other is the nonlinear eigenvalue problem with three point boundary condition.Through constructing a continuous mapping, we connect nonlinear eigenvalue problem with linear eigenvalue problem, then we can proof that the perturbed operator still have countable eigenvalues, and the existence of its eigenfunction.