Kapešić Aleksandra B.; Manojlovic Jelena V.: Decreasing solutions of cyclic second-order difference systems. (2025)
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The existence and asymptotic behavior of positive decreasing solutions to the cyclic second-order nonlinear difference system ∆(pi(n)|∆xi(n)| αi−1∆xi(n)) = qi(n)|xi+1(n + 1)| βi−1 xi+1(n + 1), i = 1, N, are studied, where xN+1 = x1, pi = {pi(n)} and qi = {qi(n)} are positive real sequences, and the constants αi and βi , i = 1, N are positive and satisfy the sublinear condition α1α2 · . . . · αN > β1β2 · . . . · βN. Two distinct types of positive decreasing solutions are considered, depending on whether the series ∑ n=1 pi(n) −1/αi is divergent or convergent. In the first case, necessary and sufficient conditions for the existence of solutions tending to a positive constant as well as solutions tending to zero, while their associated quasi-differences approach a nonzero limit, are rigorously derived using fixed point techniques. In the second case, the analysis is focused on solutions whose components and quasi-differences both tend to zero. Under the additional assumption that the coefficient sequences are regularly varying, necessary and sufficient conditions for the existence of such solutions are obtained, and their precise asymptotic behavior is determined using the theory of discrete regular variation.
| Mű típusa: | Folyóirat |
|---|---|
| Folyóirat/könyv/kiadvány címe: | Electronic journal of qualitative theory of differential equations |
| Dátum: | 2025 |
| Szám: | 46 |
| ISSN: | 1417-3875 |
| Oldalszám: | 25 |
| Nyelv: | angol |
| Kiadás helye: | Szeged |
| DOI: | 10.14232/ejqtde.2025.1.46 |
| Kulcsszavak: | Differenciaegyenlet-rendszer - ciklikus, Emden-Fowler típusú differenciaegyenlet, Differenciaegyenlet - nemlineáris |
| Megjegyzések: | Bibliogr.: p. 22-25. ; összefoglalás angol nyelven |
| Szakterület: | 01. Természettudományok 01. Természettudományok > 01.01. Matematika |
| Feltöltés dátuma: | 2025. nov. 20. 09:10 |
| Utolsó módosítás: | 2025. nov. 20. 09:10 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/88926 |
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