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Missouri University of Science and Technology
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Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner
Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.