Angelo B. Mingarelli
Abstract:
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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