A. A. Abramov, A. Aslanyan
Self-Adjoint Non-Linear Eigenvalue Problems 
for Linear Hamiltonian Systems
(103K, LaTeX 2e)

ABSTRACT.  A method for finding eigenvalues (EVs) and eigenfunctions 
of a self-adjoint differential problem has been developed. 
A two-point boundary value problem for a linear Hamiltonian 
ODE system is considered in a finite interval and on a half-line; 
a spectral parameter is involved into the system non-linearly. 
Following the proposed technique one can calculate all 
the EVs lying in a given interval (counting for their 
multiplicities). The method is based on oscillation 
properties of the system and essentially uses monotone dependence 
of its matrix on a spectral parameter. The numerical procedure 
includes a new version of the transfer (pivotal condensation) 
method. The method has been applied to several problems occurring 
in the shell theory; numerical results are also presented.