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 u0-positive operators with respect to a cone in a Banach space is applied to eigenvalue problems associated with the second order $\Delta$-differential equation (often referred to as a differential equation on a measure chain) given by
$y^{\Delta\Delta}(t)+\lambda p(t)y(\sigma(t))=0$, $t\in[0,1]$,
satisfying the boundary conditions $y(0)=0=y(\sigma^2(1))$. 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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