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.

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