### Abstract

Language | English |
---|---|

Pages | 315-345 |

Number of pages | 31 |

Journal | Journal of Differential Equations |

Volume | 171 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2001 |

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### Keywords

- nonlinear eigenvalue problem
- spectral density
- block operator matrix
- numerical mathematics
- differential equations

### Cite this

*Journal of Differential Equations*,

*171*(2), 315-345. https://doi.org/10.1006/jdeq.2000.3841

}

*Journal of Differential Equations*, vol. 171, no. 2, pp. 315-345. https://doi.org/10.1006/jdeq.2000.3841

**A spectral theory for a λ-rational Sturm-Liouville problem.** / Adamjan, V.; Langer, Heinz; Langer, M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A spectral theory for a λ-rational Sturm-Liouville problem

AU - Adamjan, V.

AU - Langer, Heinz

AU - Langer, M.

PY - 2001/2

Y1 - 2001/2

N2 - We consider the regular Sturm-Liouville problem y″−py+(λ+q/(u−λ)) y=0, which contains the eigenvalue parameter rationally. Under certain assumptions on p, q, and u it is shown that the spectrum of the problem consists of a continuous component (the range of the function u), discrete eigenvalues, and possibly a finite number of embedded eigenvalues. In the considered situation the continuous spectrum is absolutely continuous, and explicit formulas for the spectral density and the corresponding Fourier transform are given.

AB - We consider the regular Sturm-Liouville problem y″−py+(λ+q/(u−λ)) y=0, which contains the eigenvalue parameter rationally. Under certain assumptions on p, q, and u it is shown that the spectrum of the problem consists of a continuous component (the range of the function u), discrete eigenvalues, and possibly a finite number of embedded eigenvalues. In the considered situation the continuous spectrum is absolutely continuous, and explicit formulas for the spectral density and the corresponding Fourier transform are given.

KW - nonlinear eigenvalue problem

KW - spectral density

KW - block operator matrix

KW - numerical mathematics

KW - differential equations

U2 - 10.1006/jdeq.2000.3841

DO - 10.1006/jdeq.2000.3841

M3 - Article

VL - 171

SP - 315

EP - 345

JO - Journal of Differential Equations

T2 - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -