On quasi-periodic solutions of forced higher order nonlinear difference equations
Consider the following higher order difference equation x(n + 1) = f(n, x(n)) + g(n, x(n − k)) + b(n), n = 0, 1, . . . where f(n, x), g(n, x) : {0, 1, . . . } × [0, ∞) → [0, ∞) are continuous functions in x and periodic functions with period ω in n, {b(n)} is a real sequence, and k is a nonnegative...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2020
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciaegyenlet |
| doi: | 10.14232/ejqtde.2020.1.6 |
| Online Access: | http://acta.bibl.u-szeged.hu/69510 |
| Tartalmi kivonat: | Consider the following higher order difference equation x(n + 1) = f(n, x(n)) + g(n, x(n − k)) + b(n), n = 0, 1, . . . where f(n, x), g(n, x) : {0, 1, . . . } × [0, ∞) → [0, ∞) are continuous functions in x and periodic functions with period ω in n, {b(n)} is a real sequence, and k is a nonnegative integer. We show that under proper conditions, every nonnegative solution of the equation is quasi-periodic with period ω. Applications to some other difference equations derived from mathematical biology are also given. |
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| ISSN: | 1417-3875 |