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Hyers-Ulam stability of higher-order Cauchy-Euler dynamic equations on time scales
Douglas R. Anderson
We establish the stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales in the sense of Hyers and Ulam. That is, if an approximate solution…
Second-order linear constant coefficient dynamic equations with polynomial forcing on time scales
Douglas R. Anderson
A general solution for a second-order linear constant coefficient dynamic equation with polynomial forcing on time scales is given.
Young's integral inequality with upper and lower bounds
Douglas R. Anderson, Steven Noren, Brent Perreault
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that th…
Unifying discrete and continuous Weyl-Titchmarsh theory via a class of linear Hamiltonian systems on Sturmian time scales
Douglas R. Anderson
In this study, we are concerned with introducing Weyl-Titchmarsh theory for a class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian time scales. After deve…
Spectral Theory for Second-Order Vector Equations on Finite Time-Varying Domains
Douglas R. Anderson
In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-val…
Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems on Sturmian time scales
Douglas R. Anderson
We study non-self-adjoint Hamiltonian systems on Sturmian time scales, defining Weyl-Sims sets, which replace the classical Weyl circles, and a matrix-valued function on suitab…