Cabada Fernández, AlbertoOtero Espinar, María VictoriaRodríguez Vivero, Dolores2020-02-032020-02-032005Cabada, A., Otero-Espinar, V. & Rodríguez-Vivero, D. Stability of periodic solutions of first-order difference equations lying between lower and upper solutions. Adv Differ Equ 2005, 865865 (2005)1687-1839http://hdl.handle.net/10347/20651We prove that if there exists α ≤ β, a pair of lower and upper solutions of the first-order iscrete periodic problem Δu(n) = f(n,u(n)); n ∈ IN ≡ {0, . . . ,N −1}, u(0) = u(N), with f a continuous N-periodic function in its first variable and such that x + f (n,x) is strictly increasing in x, for every n ∈ IN, then, this problem has at least one solution such that its N-periodic extension to N is stable. In several particular situations, we may claim that this solution is asymptotically stable.eng© 2005, Os Autores. Baixo Licencia Creative Commons Attribution License 4.0https://creativecommons.org/licenses/by/4.0/journal article10.1155/ADE.2005.3331687-1847open access