Multiple positive periodic solutions for nonlinear first order functional difference equations

Abstract

Sufficient conditions have been obtained for the existence of at least three positive T-periodic solutions for the first order functional difference equations of the forms Δx(n) = −a(n)x(n) + λb(n)f(n, x(h(n))) and Δx(n) = a(n)x(n) − λb(n)f(n, x(h(n))). Leggett-Williams multiple fixed point theorem have been used to prove our results. We have applied our results to some mathematical models in population dynamics and obtained some interesting results. The results are new in the literature.