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An asymptotic result for some delay difference equations with continuous variable
Advances in Difference Equations volume 2004, Article number: 679264 (2004)
We consider a nonhomogeneous linear delay difference equation with continuous variable and establish an asymptotic result for the solutions. Our result is obtained by the use of a positive root with an appropriate property of the so called characteristic equation of the corresponding homogeneous linear (autonomous) delay difference equation. More precisely, we show that, for any solution, the limit of a specific integral transformation of it, which depends on a suitable positive root of the characteristic equation, exists as a real number and it is given explicitly in terms of the positive root of the characteristic equation and the initial function.
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Philos, C.G., Purnaras, I.K. An asymptotic result for some delay difference equations with continuous variable. Adv Differ Equ 2004, 679264 (2004). https://doi.org/10.1155/S1687183904310058