Stević Stevo; Iričanin Bratislav; Kosmala Witold: On a special case of a difference equation with powers. (2025)
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Investigation of the long-term behaviour of solutions to the nonlinear difference equation xn+1 = A + x p n−m x r n−k , n ∈ N0, where A, p, q ∈ R, k, m ∈ N0, k ̸= m, was proposed by S. Stevi´c about twenty years ago. A very special case of the equation (p = 1, r = 2, m = 0) has been recently considered in [J. Appl. Math. Comput. 67(2021), 423–437]. We show that the main results therein are known or have some inaccuracies. Among other things, we show that the boundedness result therein is a consequence of some known results and using one of our previous methods we give a better upper bound for positive solutions to the equation, show that the proof of the global convergence result therein is not correct and provide a complete proof of a generalization, and also show that the results on semi-cycles of positive solutions are not correct and present some correct ones. Several comments are also given and some analyses are conducted.
| Mű típusa: | Folyóirat |
|---|---|
| Folyóirat/könyv/kiadvány címe: | Electronic journal of qualitative theory of differential equations |
| Dátum: | 2025 |
| Szám: | 15 |
| ISSN: | 1417-3875 |
| Oldalszám: | 19 |
| Nyelv: | angol |
| Kiadás helye: | Szeged |
| DOI: | 10.14232/ejqtde.2025.1.15 |
| Kulcsszavak: | Differenciálegyenlet |
| Megjegyzések: | Bibliogr.: p. 15-19. ; összefoglalás angol nyelven |
| Szakterület: | 01. Természettudományok 01. Természettudományok > 01.01. Matematika |
| Feltöltés dátuma: | 2025. nov. 19. 12:56 |
| Utolsó módosítás: | 2025. nov. 19. 12:56 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/88895 |
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