tailieunhanh - Báo cáo hóa học: "OSCILLATION OF A LOGISTIC DIFFERENCE EQUATION WITH SEVERAL DELAYS"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: OSCILLATION OF A LOGISTIC DIFFERENCE EQUATION WITH SEVERAL DELAYS | OSCILLATION OF A LOGISTIC DIFFERENCE EQUATION WITH SEVERAL DELAYS L. BEREZANSKY AND E. BRAVERMAN Received 13 January 2005 Revised 19 July 2005 Accepted 21 July 2005 For a delay difference equation N n 1 - N n N n Xk 1 ak n 1 - N gk n K ak n 0 gk n n K 0 a connection between oscillation properties of this equation and the corresponding linear equations is established. Explicit nonoscillation and oscillation conditions are presented. Positiveness of solutions is discussed. Copyright 2006 L. Berezansky and E. Braverman. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Difference equations provide an important framework for analysis of dynamical phenomena in biology ecology economics and so forth. For example in population dynamics discrete systems adequately describe organisms for which births occur in regular usually short breeding seasons. Recently the problem of oscillation and nonoscillation of solutions for nonlinear delay difference equations has been intensively studied see monographs 1 2 7 9 and references therein for more details. In this paper we study the following nonlinear difference equation N n 1 - N n N n m ak n 1 -k 1 N gk n K ak n 0 gk n n K 0 where the number gk n is an integer positive or negative for every n and k. Equation describes populations that die out completely at each generation and have birth rates that saturate for large population sizes N K. Equation is a discrete analogue Hindawi Publishing Corporation Advances in Difference Equations Volume 2006 Article ID 82143 Pages 1-12 DOI ADE 2006 82143 2 Oscillation of a logistic equation of the well-known logistic differential equation with several delays . N gk t N t N t ỵ ak t 1 - g i . k 1 K Oscillation properties of were considered in 3 4 12 . In 9 oscillation properties of another .