Electron. J. Differential Equations, Vol. 2017 (2017), No. 50, pp. 1-3.

Eigenvalues of Sturm-Liouville operators and prime numbers

Rauf Amirov, Ibrahim Adalar

We show that there is no function $q(x)\in L_2(0,1)$ which is the potential of a Sturm-Liouville problem with Dirichlet boundary condition whose spectrum is a set depending nonlinearly on the set of prime numbers as suggested by Mingarelli [7].

Submitted June 1, 2016. Published February 20, 2017.
Math Subject Classifications: 34B05, 34B07, 11Z05
Key Words: Sturm-Liouville; spectrum; prime numbers.

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Rauf Amirov
Department of Mathematics
Faculty of Sciences
Cumhuriyet University
58140 Sivas, Turkey
email: emirov@cumhuriyet.edu.tr
Ibrahim Adalar
Zara Ahmet Cuhadaroglu Vocational School
Cumhuriyet University
Zara/Sivas, Turkey
email: iadalar@cumhuriyet.edu.tr

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