Eigenvalue comparisons for differential equations on a measure chain.

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 #-differential equation (often referred to as a differential equation on a measure chain) given by y ## (t)+#p(t)y(#(t)) = 0,t#[0, 1], satisfying the boundary conditions y(0) = 0 = y(# 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.