Stability of periodic solutions of first-order difference equations lying between lower and upper solutions. Issue 3 (27th September 2005) - Cabada, Alberto; Otero-Espinar, Victoria; Rodríguez-Vivero, Dolores
Abstract : We prove that if there existsα ≤ β, a pair of lower and upper solutions of the first-order discrete periodic problemΔ u ( n ) = f ( n, u ( n ) ) ; n ∈ I N ≡ 0, …, N − 1 , u ( 0 ) = u ( N ), withf a continuousN -periodic function in its first variable and such thatx + f ( n, x ) is strictly increasing inx, for everyn ∈ I N, then, this problem has at least one solution such that itsN -periodic extension toℕ is stable. In several particular situations, we may claim that this solution is asymptotically stable.