Renormalized oscillation theory for symplectic eigenvalue problems with nonlinear dependence on the spectral parameter

In this paper, we establish new renormalized oscillation theorems for discrete symplectic eigenvalue problems with Dirichlet boundary conditions. These theorems present the number of finite eigenvalues of the problem in the arbitrary interval using the number of focal points of a transformed conjoin...

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Vydáno v:Journal of difference equations and applications Ročník 26; číslo 4; s. 458 - 487
Hlavní autor: Elyseeva, Julia
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 02.04.2020
Taylor & Francis Ltd
Témata:
Boundary conditions
comparative index
Dirichlet problem
Discrete eigenvalue problem
Eigenvalues
Parameters
renormalized oscillation theory
Spectra
symplectic difference system
Theorems
ISSN:1023-6198, 1563-5120
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Shrnutí:In this paper, we establish new renormalized oscillation theorems for discrete symplectic eigenvalue problems with Dirichlet boundary conditions. These theorems present the number of finite eigenvalues of the problem in the arbitrary interval using the number of focal points of a transformed conjoined basis associated with Wronskian of two principal solutions of the symplectic system evaluated at the endpoints a and b. We suppose that the symplectic coefficient matrix of the system depends nonlinearly on the spectral parameter and that it satisfies certain natural monotonicity assumptions. In our treatment, we admit possible oscillations in the coefficients of the symplectic system by incorporating their non-constant rank with respect to the spectral parameter.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2020.1748020