Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter

Volume 9, Issue 2, pp 435--442
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Authors

Deniz Katar - Faculty of Sciences, Department of Mathematics, Ankara University, Ankara, Turkey. Murat Olgun - Faculty of Sciences, Department of Mathematics, Ankara University, Ankara, Turkey. Cafer Coskun - Faculty of Sciences, Department of Mathematics, Ankara University, Ankara, Turkey.

Abstract

Let $L$ denote the operator generated in$L_2(\mathbb{R}_+;E)$ by the differential expression $l(y) = -y'' + Q(x)y; \qquad x \in \mathbb{R}_+$; and the boundary condition $(A_0 + A_1\lambda)Y' (0; \lambda) - (B_0 + B_1\lambda)Y (0; \lambda) = 0$ , where $Q$ is a matrix-valued function and $A_0; A_1; B_0; B_1$ are non-singular matrices, with $A_0B_1 - A_1B_0 \neq 0$: In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of $L$. In particular, we obtain the conditions on q under which the operator $L$ has a finite number of the eigenvalues and the spectral singularities.

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ISRP Style

Deniz Katar, Murat Olgun, Cafer Coskun, Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 2, 435--442

AMA Style

Katar Deniz, Olgun Murat, Coskun Cafer, Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter. J. Nonlinear Sci. Appl. (2016); 9(2):435--442

Chicago/Turabian Style

Katar, Deniz, Olgun, Murat, Coskun, Cafer. "Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter." Journal of Nonlinear Sciences and Applications, 9, no. 2 (2016): 435--442

Keywords

• Eigenvalues
• spectral singularities
• spectral analysis
• Sturm-Liouville operator

•  34B24
•  47A10
•  34L40

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