Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter
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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
- non-selfadjoint matrix operator
MSC
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