Geodesic
The boundedness of non-autonomous nonlinear time-varying delay difference equations subject to external disturbances and its applications
Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 2, pp. 52-68

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First, we employ fixed point theory and compute some difference inequalities to derive some new results on the existence of positive solutions and the equi-boundedness of solutions. Second, we derive a sufficient condition for the ultimate boundedness of solutions. Third, we apply the obtained results to some discrete population models. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.
Keywords: Fixed point theorem, contraction mapping, nonlinear difference equations, boundedness, time-varying delays. 
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     author = {D. C. Huong},
     title = {The boundedness of non-autonomous nonlinear time-varying delay difference equations subject to external disturbances and its applications},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {52--68},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2020_8_2_a3/}
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D. C. Huong. The boundedness of non-autonomous nonlinear time-varying delay difference equations subject to external disturbances and its applications. Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 2, pp. 52-68. http://geodesic.mathdoc.fr/item/EJMCA_2020_8_2_a3/