Eigenvalue Comparisons for Differential Equations on a Measure Chain
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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.
CitationChyan, C. J., Davis, J. M., Henderson, J., & Yin, W. K. C. (1998). Eigenvalue comparisons for differential equations on a measure chain. Electronic Journal of Differential Equations, 1998(35), pp. 1-7.
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