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

Katar, Deniz¹ ; Olgun, Murat¹ ; Coskun, Cafer¹

¹ Faculty of Sciences, Department of Mathematics, Ankara University, Ankara, Turkey

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 2, p. 435-442.

Résumé

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.

Détail

DOI : 10.22436/jnsa.009.02.09

Classification : 34B24, 47A10, 34L40
Keywords: Eigenvalues, spectral singularities, spectral analysis, Sturm-Liouville operator, non-selfadjoint matrix operator

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