Comparison of eigenvalues for lidstone boundary value problems on a measure chain (preprint)

The theory of u0-positive operators with respect to a cone in a Banach space is applied to the class of even-order differential equation on measure chains , satisfying the lidstone boundary conditions xΔ2i(0) = 0, 0 < i ≤ m − 1; xΔ2j(σ2(1)) = 0, 0 ≤ j ≤ m − 1. The existence of a smallest positive eigenvalue is obtained and then a theorem is established comparing the smallest positive eigenvalues for two problems of this type.