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

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