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Investigation of the spectrum of singular Sturm–Liouville operators on unbounded time scales

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Abstract

In this article, we consider the self-adjoint singular operators associated with the Sturm–Liouville expression

$$\begin{aligned} Ly:=-\left[ p\left( t\right) y^{\Delta }\left( t\right) \right] ^{\nabla }+q\left( t\right) y\left( t\right) ,\ t\in (-\infty ,\infty )_{\mathbb {T}}. \end{aligned}$$

on time scale \(\mathbb {T}\). Some conditions are given for this operator to have a discrete spectrum. Further, we investigate the continuous spectrum of this operator. We also prove that the regular Sturm–Liouville operator on time scale is semi-bounded from below which is not studied in literature yet.

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Authors and Affiliations

  1. Department of Mathematics, Süleyman Demirel University, 32260, Isparta, Turkey

    Bilender P. Allahverdiev

  2. Department of Mathematics, Mehmet Akif Ersoy University, 15030, Burdur, Turkey

    Hüseyin Tuna

Authors
  1. Bilender P. Allahverdiev
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  2. Hüseyin Tuna
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Correspondence to Hüseyin Tuna.

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Allahverdiev, B.P., Tuna, H. Investigation of the spectrum of singular Sturm–Liouville operators on unbounded time scales. São Paulo J. Math. Sci. 14, 327–340 (2020). https://doi.org/10.1007/s40863-019-00137-4

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  • DOI: https://doi.org/10.1007/s40863-019-00137-4

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