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 . 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
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