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Linear perturbations of a nonoscillatory second-order dynamic equation. (English) Zbl 1187.34127
The authors consider a non-oscillatory second-order linear dynamic equation on a time scale, and obtain non-oscillatory properties for this equation. Using the perturbation theory, the authors compare this equation with a given linear dynamic equation, which is non-oscillatory (the recessive solution and dominant solution are characterized), and obtain that the perturbed equation has the same asymptotic properties as the unperturbed equation. This results is a generalization of a paper by Trench for differential equation, when the time scale is reduced to integer numbers, the obtained result is new for difference equation.

MSC:
34N05Dynamic equations on time scales or measure chains
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A30Linear ODE and systems, general
39A10Additive difference equations
34D05Asymptotic stability of ODE
34D10Stability perturbations of ODE
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