Positive Solutions of Advanced Differential Systems-Reference-Cited by-同舟云学术

Positive Solutions of Advanced Differential Systems

Published:2013 Issue: Volume:2013 Page:1-7
ISSN:1537-744X
Container-title:The Scientific World Journal
language:en
Short-container-title:The Scientific World Journal

Author:

Diblík Josef¹²,Kúdelčíková Mária³

Affiliation:

1. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 602 00 Brno, Czech Republic

2. Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00 Brno, Czech Republic

3. Department of Mathematics, University of Žilina, Univerzitná 8215/1, 010 26 Žilina, Slovakia

Abstract

We study asymptotic behavior of solutions of general advanced differential systemsy˙(t)=F(t,yt), whereF:Ω→ℝnis a continuous quasi-bounded functional which satisfies a local Lipschitz condition with respect to the second argument andΩis a subset inℝ×Crn,Crn:=C([0,r],ℝn),yt∈Crn, andyt(θ)=y(t+θ),θ∈[0,r]. A monotone iterative method is proposed to prove the existence of a solution defined fort→∞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.

Funder

Czech Grant Agency

Publisher

Hindawi Limited

Subject

General Environmental Science,General Biochemistry, Genetics and Molecular Biology,General Medicine

Link

http://downloads.hindawi.com/journals/tswj/2013/613832.pdf

Reference6 articles.

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