Electron. J. Differential Equations, Vol. 2017 (2017), No. 264, pp. 1-13.

Inequalities among eigenvalues of Sturm Liouville equations with periodic coefficients

Yaping Yuan, Jiong Sun, Anton Zettl

Abstract:
It is well known that for h-periodic coefficients, every periodic eigenvalue on every interval [a,a+kh], k=2,3,4,..., is also an eigenvalue on the interval [a,a+h] of a periodic, semi-periodic or complex self-adjoint boundary condition. Here we give an explicit 1-1 correspondence between these eigenvalues.

Submitted July 28, 2017. Published October 19, 2017.
Math Subject Classifications: 34B20, 34B24, 47B25.
Key Words: Periodic coefficients; eigenvalue inequalities and equalities.

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Yaping Yuan
School of Mathematical Sciences
Inner Mongolia University
Hohhot, China
email: yaping_yyp@qq.com
Jiong Sun
School of Mathematical Sciences
Inner Mongolia University
Hohhot, China
email: 272454707@qq.com
Anton Zettl
Mathematics Deparment
Northern Illinois University
DeKalb, IL, USA
email: zettl@msn.com

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