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Higher Order Dynamic Equations On Measure Chains: Wronskians, Disconjugacy, And Interpolating Families Of Functions, Martin Bohner, Paul Eloe
Higher Order Dynamic Equations On Measure Chains: Wronskians, Disconjugacy, And Interpolating Families Of Functions, Martin Bohner, Paul Eloe
Paul W. Eloe
This paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations, which cover simultaneously as special cases (among others) both differential equations and difference equations. We also define Markov, Fekete, and Descartes interpolating systems of functions. The main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator. The results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference …
Exponential Stability In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef Raffoul, Christopher Tisdell
Exponential Stability In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef Raffoul, Christopher Tisdell
Youssef N. Raffoul
We are interested in the exponential stability of the zero solution of a functional dynamic equation on a time scale, a nonempty closed subset of real numbers. The approach is based on suitable Lyapunov functionals and certain inequalities. We apply our results to obtain exponential stability in Volterra integrodynamic equations on time scales.