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 Δ-differential equation (often referred to as a differential equation on a measure chain) given by yΔΔ(t) + λp(t) y(σ(t)) = 0, t ∈ [0, 1], satisfying the boundary conditions y(0) = 0 = y(σ2(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.
Relation:
Electronic Journal of Differential Equations 35, pp.1-7
