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.
S. Stevic and M. Bohner, "Trench's Perturbation Theorem for Dynamic Equations," Discrete Dynamics in Nature and Society, Hindawi Publishing Corporation, Jan 2007.
The definitive version is available at https://doi.org/10.1155/2007/75672
Mathematics and Statistics
Keywords and Phrases
Dynamics; Perturbation (Mathematics)
Article - Journal
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