A General Version of the Retract Method for Discrete Equations  

作　　者：Josef DIBLíK Irena RzIKOV Miroslava RZIKOV 

机构地区：[1]Department of Mathematics,Faculty of Electrical Engineering and Communication,Brno University of Technology,Technická 8,616 00 Brno,Czech Republic [2]Department of Applied Mathematics,Faculty of Science,Cilina University,Hurbanova 15,010 26 Cilina,Slovak Republic

出　　处：《Acta Mathematica Sinica,English Series》2007年第2期341-348,共8页数学学报（英文版）

基　　金：supported by the Grant 201/04/0580 of the Czech Grant Agency(Prague);by the Grant No 1/0026/03 and No 1/3238/06 of the Grant Agency of Slovak Republic(VEGA)

摘　　要：We study a problem concerning the compulsory behavior of the solutions of systems of discrete equations u（k ＋ 1） = F（k, u（k））, k ∈ N（a） = {a, a ＋ 1, a ＋ 2 }, a ∈ N,N= {0, 1,... } and F ： N（a） × R^n→R^n. A general principle for the existence of at least one solution with graph staying for every k ∈ N（a） in a previously prescribed domain is formulated. Such solutions are defined by means of the corresponding initial data and their existence is proved by means of retract type approach. For the development of this approach a notion of egress type points lying on the defined boundary of a given domain and with respect to the system considered is utilized. Unlike previous investigations, the boundary can contain points which are not points of egress type, too. Examples are inserted to illustrate the obtained result.We study a problem concerning the compulsory behavior of the solutions of systems of discrete equations u（k ＋ 1） = F（k, u（k））, k ∈ N（a） = {a, a ＋ 1, a ＋ 2 }, a ∈ N,N= {0, 1,... } and F ： N（a） × R^n→R^n. A general principle for the existence of at least one solution with graph staying for every k ∈ N（a） in a previously prescribed domain is formulated. Such solutions are defined by means of the corresponding initial data and their existence is proved by means of retract type approach. For the development of this approach a notion of egress type points lying on the defined boundary of a given domain and with respect to the system considered is utilized. Unlike previous investigations, the boundary can contain points which are not points of egress type, too. Examples are inserted to illustrate the obtained result.

关 键 词：discrete equation consequent point RETRACT 

分 类 号：O175[理学—数学]