- 98-637 A. A. Abramov, A. Aslanyan
- Self-Adjoint Non-Linear Eigenvalue Problems
for Linear Hamiltonian Systems
(103K, LaTeX 2e)
Oct 12, 98
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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.