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**Principal functions of non-selfadjoint Sturm-Liouville problems with eigenvalue-dependent boundary conditions.**
*(English)*
Zbl 1222.34102

Summary: We consider the operator \(L\) generated in \(L^2(\mathbb R_+)\) by the differential expression

\[ l(y) = -y^n + q(x)y,\quad x \in \mathbb R_+ := [0, \infty) \]

and the boundary condition

\[ y'(0)/y(0) = \alpha_0 + \alpha_1\lambda + \alpha_2\lambda^2, \]

where \(q\) is a complex-valued function and \(\alpha_i \in \mathbb C, i = 0, 1, 2\) with \(\alpha_2 \neq 0\) . We obtain the properties of the principal functions corresponding to the spectral singularities of \(L\) .

\[ l(y) = -y^n + q(x)y,\quad x \in \mathbb R_+ := [0, \infty) \]

and the boundary condition

\[ y'(0)/y(0) = \alpha_0 + \alpha_1\lambda + \alpha_2\lambda^2, \]

where \(q\) is a complex-valued function and \(\alpha_i \in \mathbb C, i = 0, 1, 2\) with \(\alpha_2 \neq 0\) . We obtain the properties of the principal functions corresponding to the spectral singularities of \(L\) .

### MSC:

34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |

34B24 | Sturm-Liouville theory |

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\textit{N. Yokuş}, Abstr. Appl. Anal. 2011, Article ID 358912, 12 p. (2011; Zbl 1222.34102)

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### References:

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