Electron. J. Diff. Equ., Vol. 2011 (2011), No. 123, pp. 1-4.

A note on Sturm-Liouville problems whose spectrum is the set of prime numbers

Angelo B. Mingarelli

We show that there is no classical regular Sturm-Liouville problem on a finite interval whose spectrum consists of infinitely many distinct primes numbers. In particular, this answers in the negative a question raised by Zettl in his book [9]. We also show that there may exist such a problem if the parameter dependence is nonlinear.

Submitted August 9, 2011. Published September 27, 2011.
Math Subject Classifications: 34B05, 34B07, 11Z05.
Key Words: Sturm-Liouville; spectrum; prime numbers

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Angelo B. Mingarelli
School of Mathematics and Statistics
Carleton University, Ottawa, Ontario, K1S 5B6, Canada
email: amingare@math.carleton.ca

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