Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2013, Article ID 613832, 7 pages
Research Article

Positive Solutions of Advanced Differential Systems

1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 602 00 Brno, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00 Brno, Czech Republic
3Department of Mathematics, University of Žilina, Univerzitná 8215/1, 010 26 Žilina, Slovakia

Received 24 June 2013; Accepted 13 July 2013

Academic Editors: J. Banaś, M. M. Cavalcanti, N. Kallur, and M. Mansour

Copyright © 2013 Josef Diblík and Mária Kúdelčíková. 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.


We study asymptotic behavior of solutions of general advanced differential systems , where is a continuous quasi-bounded functional which satisfies a local Lipschitz condition with respect to the second argument and is a subset in , , , and , . A monotone iterative method is proposed to prove the existence of a solution defined for with the graph coordinates lying between graph coordinates of two (lower and upper) auxiliary vector functions. This result is applied to scalar advanced linear differential equations. Criteria of existence of positive solutions are given and their asymptotic behavior is discussed.