STABILITY OF PERIODIC SOLUTIONS OF FIRST-ORDER DIFFERENCE EQUATIONS LYING BETWEEN LOWER AND UPPER SOLUTIONS

摘要

We prove that if there exists α≤β, a pair of lower and upper solutions of the first-order discrete periodic problem △u(n) =f(n,u(n));n∈IN ≡{O,...,N-1}, u(o) = u{N), with / a continuous N-periodic function in its first variable and such that x + f(n,x) is strictly increasing in x, for every n G 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.