Spectral Theory for Second-Order Vector Equations on Finite Time-Varying Domains

2010/01/22 by Douglas R. Anderson, Anderson, Douglas R.
Engineering · Mathematics · #15A24 #34B24 #34N05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1001.4010

openalex publication_date 2010/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the domain is non-uniform but finite. A concept of self-adjointness of the boundary conditions is introduced. The self-adjointness of the corresponding dynamic operator is discussed on a suitable admissible function space, and fundamental spectral results are obtained. The dual orthogonality of eigenfunctions is shown in a special case. Extensions to even-order Sturm-Liouville dynamic equations, linear Hamiltonian and symplectic nabla systems on general time scales are also discussed.

Citations

• A Unified Approach to High-Gain Adaptive Controllers

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