Eigenvalue Comparisons for Differential Equations on a Measure Chain
Date
1998-12-19
Authors
Chyan, Chuan Jen
Davis, John M.
Henderson, Johnny
Yin, William K. C.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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 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.
Description
Keywords
Measure chain, Eigenvalue problem
Citation
Chyan, C. J., Davis, J. M., Henderson, J., & Yin, W. K. C. (1998). Eigenvalue comparisons for differential equations on a measure chain. <i>Electronic Journal of Differential Equations, 1998</i>(35), pp. 1-7.
Rights
Attribution 4.0 International