Geodesic
A note on Sturm-Liouville problems whose spectrum is the set of prime numbers
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34B05, 34B07, 11Z05
Keywords: Sturm-Liouville, spectrum, prime numbers 
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     author = {Mingarelli, Angelo B.},
     title = {A note on {Sturm-Liouville} problems whose spectrum is the set of prime numbers},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a91/}
}
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Mingarelli, Angelo B. A note on Sturm-Liouville problems whose spectrum is the set of prime numbers. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a91/