Open AccessStability of periodic solutions of first-order difference equations lying between lower and upper solutions
Author(s) -
Alberto Cabada,
Victoria Otero-Espinar,
Dolores Rodríguez-Vivero
Publication year - 2005
Publication title -
advances in difference equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.67
H-Index - 51
eISSN - 1687-1847
pISSN - 1687-1839
DOI - 10.1155/ade.2005.333
Subject(s) - mathematics , ordinary differential equation , partial differential equation , stability (learning theory) , mathematical analysis , order (exchange) , differential equation , computer science , finance , machine learning , economics
We prove that if there exists α≤β, a pair of lower and upper solutions of the first-order discrete 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