A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition

A nonlinear eigenvalue problem for a self-adjoint Hamiltonian system of differential equations is examined on an infinite half-line. It is assumed that the original data (that is, the system matrix and the matrix of boundary conditions) satisfy certain monotonicity conditions for the spectral parameter. In addition to the initial condition and the requirement that the solution be bounded on infinity, a redundant nonlocal condition specified by a Stieltjes integral is imposed. In order to make the resulting problem nontrivially solvable, it is replaced by an auxiliary problem, which is consistent subject to all the above conditions. This auxiliary problem is examined, and a numerical method that solves it is given.