On the general nonlinear self-adjoint eigenvalue problem for systems of ordinary differential equations with singularities |
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Authors: | A. A. Abramov V. I. Ul’yanova L. F. Yukhno |
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Affiliation: | 1.Dorodnicyn Computing Center,Russian Academy of Sciences,Moscow,Russia;2.Institute of Mathematical Modeling,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | A nonlinear self-adjoint eigenvalue problem for the general linear system of ordinary differential equations is examined on an unbounded interval. A method is proposed for the approximate reduction of this problem to the corresponding problem on a finite interval. Under the assumption that the initial data are monotone functions of the spectral parameter, a method is given for determining the number of eigenvalues lying on a prescribed interval of this parameter. No direct calculation of eigenvalues is required in this method. |
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