On the number of an eigenvalue of a general nonlinear self-adjoint spectral problem for systems of ordinary differential equations

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...

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Veröffentlicht in:Differential equations Jg. 46; H. 7; S. 1063 - 1067
Hauptverfasser: Abramov, A. A., Ul’yanova, V. I., Yukhno, L. F.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht SP MAIK Nauka/Interperiodica 01.07.2010
Springer Nature B.V
Schlagworte:
Boundary conditions
Boundary value problems
Computation
Difference and Functional Equations
Differential equations
Eigenvalues
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear systems
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Short Communications
Spectra
Studies
Cauchy Problem
Nondecreasing Function
Spectral Problem
Spectral Parameter
Hamiltonian System
ISSN:0012-2661, 1608-3083
Online-Zugang:Volltext
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Zusammenfassung: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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ISSN:0012-2661
1608-3083
DOI:10.1134/S001226611007013X