Along the lines of Atkinson [3], a spectral theorem is proved for the boundary value problem, where f(t) is real-valued and P(t),B(t) are symmetric matrices, with B(t) positive definite. A suitable rotation index associated to the system is used to highlight the connections between the eigenvalues and the nodal properties of the corresponding eigenfunctions.
Boscaggin, A., Garrione, M. (2010). A note on a linear spectral theorem for a class of first order systems in R2n. ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 75(75), 1-22 [10.14232/ejqtde.2010.1.75].
A note on a linear spectral theorem for a class of first order systems in R2n
BOSCAGGIN, ALBERTO;GARRIONE, MAURIZIO
2010
Abstract
Along the lines of Atkinson [3], a spectral theorem is proved for the boundary value problem, where f(t) is real-valued and P(t),B(t) are symmetric matrices, with B(t) positive definite. A suitable rotation index associated to the system is used to highlight the connections between the eigenvalues and the nodal properties of the corresponding eigenfunctions.
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