On the Self-Adjoint Nonlinear Eigenvalue Problem for Hamiltonian Systems of Ordinary Differential Equations with Singularities

摘要

Certain properties of the nonlinear self-adjoint eigenvalue problem for Hamiltonian systemsof ordinary differential equations with singularities are examined. Under certain assumptions on the wayin which the matrix of the system and the matrix specifying the boundary condition at a regular pointdepend on the spectral parameter, a numerical method is proposed for determining the number of eigen-values lying on a prescribed interval of the spectral parameter.