Determination of the number of an eigenvalue of a singular nonlinear self-adjoint spectral problem for a linear Hamiltonian system of differential equations

We suggest a method for determining the number of an eigenvalue of a self-adjoint spectral problem nonlinear with respect to the spectral parameter, for some class of Hamiltonian systems of ordinary differential equations on the half-line. The standard boundary conditions are posed at zero, and the...

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Vydáno v:Differential equations Ročník 47; číslo 8; s. 1110 - 1115
Hlavní autoři: Abramov, A. A., Ul’yanova, V. I., Yukhno, L. F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht SP MAIK Nauka/Interperiodica 01.08.2011
Springer Nature B.V
Témata:
Boundary conditions
Boundary value problems
Difference and Functional Equations
Differential equations
Eigenvalues
Infinity
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
Spectra
Studies
Linear Hamiltonian System
Spectral Parameter
Hamiltonian System
Singular Problem
Hermitian Matrix
ISSN:0012-2661, 1608-3083
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Shrnutí:We suggest a method for determining the number of an eigenvalue of a self-adjoint spectral problem nonlinear with respect to the spectral parameter, for some class of Hamiltonian systems of ordinary differential equations on the half-line. The standard boundary conditions are posed at zero, and the solution boundedness condition is posed at infinity. We assume that the matrix of the system is monotone with respect to the spectral parameter. The number of an eigenvalue is determined by the properties of the corresponding nontrivially solvable homogeneous boundary value problem. For the considered class of systems, it becomes possible to compute the numbers of eigenvalues lying in a given range of the spectral parameter without finding the eigenvalues themselves.
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ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266111080052