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

STABILITY OF PERIODIC SOLUTIONS OF FIRST-ORDER DIFFERENCE EQUATIONS LYING BETWEEN LOWER AND UPPER SOLUTIONS ALBERTO CABADA, VICTORIA OTERO-ESPINAR, ´ AND DOLORES RODRIGUEZ-VIVERO Received 8 January 2004 and in revised form 2 September 2004 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 ≡ {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...