Title: Multiple positive periodic solutions for nonlinear first order functional difference equations

Authors: Seshadev Padhi, Smita Pati, Shilpee Srivastava

Addresses: Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835215, India. ' Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835215, India. ' Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835215, India

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.

Keywords: positive periodic solutions; nonlinear difference equations; first order functional difference equations; multiple fixed point theorem; mathematical modelling; population dynamics.

DOI: 10.1504/IJDSDE.2009.028037

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.1/2, pp.98 - 114

Published online: 02 Sep 2009 *

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