On the number of an eigenvalue of a general nonlinear self-adjoint spectral problem for systems of ordinary differential equations |
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Authors: | A A Abramov V I Ul’yanova L F Yukhno |
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Institution: | 1.Dorodnitsyn Computing Center,Russian Academy of Sciences,Moscow,Russia;2.Institute for Mathematical Modeling,Russian Academy of Science,Moscow,Russia |
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Abstract: | In the case of a general nonlinear self-adjoint spectral problem for systems of ordinary differential equations with boundary
conditions independent of the spectral parameter, we introduce the notion of the number of an eigenvalue. Methods for the
computation of the numbers of eigenvalues lying in a given range of the spectral parameter and for finding the eigenvalue
with a given number, which were earlier suggested by the author for Hamiltonian systems, are generalized to the considered
problem. We introduce the notion of an index of a problem for a general nontrivially solvable linear homogeneous self-adjoint
boundary value problem. |
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Keywords: | |
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