Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 35, pp. 1-7.

Title: Eigenvalue comparisons for differential equations on a measure chain
       
Authors: Chuan Jen Chyan (Tamkang Univ., Taipei, Taiwan)
 John M. Davis (Auburn Univ., Auburn, USA)
 Johnny Henderson (Auburn Univ., Auburn, USA)
 William K. C. Yin (LaGrange College, LaGrange, USA)

Abstract: 
The theory of $\mathbf{u_0}$-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 
        $$
y^{\Delta\Delta}(t)+\lambda p(t)y(\sigma(t))=0, \qquad t\in[0,1],
        $$
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