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: BOUNDARY VALUE PROBLEMS FOR FUNCTIONAL DIFFERENCE EQUATIONS ON INFINITE INTERVALS | BOUNDARY VALUE PROBLEMS FOR FUNCTIONAL DIFFERENCE EQUATIONS ON INFINITE INTERVALS MAURO MARINI SERENA MATUCCI AND PAVEL RehAk Received 27 May 2005 Accepted 29 June 2005 A general method for solving boundary value problems associated to functional difference systems on the discrete half-line is presented and applied in studying the existence of positive unbounded solutions for a system of two coupled nonlinear difference equations. A further example illustrating the method completes the paper. Copyright 2006 Mauro Marini 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 A method for solving discrete functional boundary value problems FBVPs on infinite intervals is presented and applied to study the existence of positive unbounded solutions of the coupled nonlinear difference system A rk a Axt - f k yk 1 A qk 8 A yk g k Xk 1 where A is the forward difference operator r rk q qk are positive real sequences a u I u IA-1 sgn u with A 1 and f g are real continuous functions on N X R satisfying additional assumptions that will be specified later. The sequences r q are assumed to satisfy 1 k 1 a rk TO 1 y k 1 8 q where a and 8 denote the conjugate numbers of a and 8 respectively that is 1 a 1 a 1 and 1 8 1 8 1. In the last years an increasing interest has been devoted to investigate the qualitative properties of higher order difference equations and in particular fourth order equations. Hindawi Publishing Corporation Advances in Difference Equations Volume 2006 Article ID 31283 Pages 1-14 DOI ADE 2006 31283 2 BVPs for functional difference equations They naturally appear in the discretization of a variety of physical biological and chemical phenomena such as for instance problems of elasticity deformation of structures or soil settlement see . 9 10 . We refer for instance to
