Electron. J. Diff. Eqns., Vol. 1998(1998), No. 35, pp. 1-7.
### Eigenvalue Comparisons for Differential Equations on a Measure Chain

Chuan Jen Chyan, John M. Davis,
Johnny Henderson, & William K. C. Yin

**Abstract:**

The theory of *u*_{0}-positive operators with respect to a
cone in a Banach space is applied to eigenvalue problems associated with the
second order
-differential
equation (often referred to as a differential equation on a measure chain)
given by

,
,

satisfying the boundary conditions
.
The existence of a smallest positive eigenvalue is proven and then a theorem
is established comparing the smallest positive eigenvalues for two problems
of this type.
Submitted November 23, 1998. Published December 19, 1998.

Math Subject Classification: 34B99, 39A99.

Key Words: Measure chain, eigenvalue problem

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Chuan Jen Chyan

Department of Mathematics,
Tamkang University,
Taipei, Taiwan

e-mail: chuanjen@mail.tku.edu.tw
John M. Davis

Department of Mathematics,
Auburn University,
Auburn, AL 36849 USA

e-mail: davis05@mail.auburn.edu

Johnny Henderson

Department of Mathematics,
Auburn University,
Auburn, AL 36849 USA

e-mail: hendej2@mail.auburn.edu

William K. C. Yin

Department of Mathematics,
LaGrange College,
LaGrange, GA 30240 USA

e-mail: wyin@lgc.edu

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