Open Access

Stability of periodic solutions of first-order difference equations lying between lower and upper solutions

  • Alberto Cabada1Email author,
  • Victoria Otero-Espinar1 and
  • Dolores Rodríguez-Vivero1
Advances in Difference Equations20052005:865865

DOI: 10.1155/ADE.2005.333

Received: 8 January 2004

Published: 27 September 2005

Abstract

We prove that if there exists αβ, a pair of lower and upper solutions of the first-order discrete periodic problem Δu(n) = f(n,u(n));n I N ≡ {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 I N , then, this problem has at least one solution such that its N-periodic extension to is stable. In several particular situations, we may claim that this solution is asymptotically stable.

Authors’ Affiliations

(1)
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela

Copyright

© Cabada et al. 2005