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: Research Article On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 505324 15 pages doi 2008 505324 Research Article On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument M. Cecchi 1 Z. Dosla 2 and M. Marini1 1 Department of Electronics and Telecommunications University of Florence Via S. Marta 3 50139 Firenze Italy 2 Department of Mathematics and Statistics Masaryk University Jandckovo nam. 2a 60200 Brno Czech Republic Correspondence should be addressed to M. Cecchi Received 28 March 2008 Accepted 27 May 2008 Recommended by Martin Bohner The half-linear difference equations with the deviating argument A an Axn a sgn Axn bn xn q a sgn xn q 0 q E Z are considered. We study the role of the deviating argument q especially as regards the growth of the nonoscillatory solutions and the oscillation. Moreover the problem of the existence of the intermediate solutions is completely resolved for the classical half-linear equation q 1 . Some analogies or discrepancies on the growth of the nonoscillatory solutions for the delayed and advanced equations are presented and the coexistence with different types of nonoscillatory solutions is studied. Copyright 2008 M. Cecchi et al. 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 Consider the half-linear difference equations with the deviating argument A an Axn asgnAxn bn xn q asgnxn q 0 where A is the forward difference operator Axn xn 1 - xn a 0 q E Z and a an b bn are positive real sequences for n 0 such that Ya - f 1 f a -- n 0 TO Yb Xbn TO. n 0 A large number of papers deal with the oscillatory and asymptotic properties of several particular cases of such as the classical half-linear equation A an Axn aSgnAxn bn xn 1 aSgnxn 1 0 H 2 Advances in .
