Volume 5 Number 2 (Apr. 2015)
Home > Archive > 2015 > Volume 5 Number 2 (Apr. 2015) >
IJAPM 2015 Vol.5(2): 115-125 ISSN: 2010-362X
doi: 10.17706/ijapm.2015.5.2.115-125

Existence of Extremal Solutions of Differential Equations with Delay in Banach Spaces

Jinjun Fan, Xiaodi Li, Haydar Akca
Abstract—In this paper, by using the monotone iterative method and Daher's fixed point theorem and an inequality of noncompact measure of Monch and Von Harten, we study the existence of maximum solution and minimal solution and the iterative approximation of the following initial value problem for O.D.E with delay in Banach spaces u’ = f(t, u(t), ut), ut0 = ψ0 and give a sufficient condition of the existence of solutions of the above problem. The obtained results improve and generalize the corresponding results.

Index Terms—Banach space, measure of noncompactness, differential equation, normal cone, 2000 Mathematics Subject Classification 34G20, 47H07.

Jinjun Fan, Xiaodi Li are with School of Mathematical Sciences, Shandong Normal University, Ji'nan, 250014, Shandong, China.
Haydar Akca is with the Department of Mathematics, College of Arts and Science faculty, Abu Dhabi University, UAE.

Cite: Jinjun Fan, Xiaodi Li, Haydar Akca, "Existence of Extremal Solutions of Differential Equations with Delay in Banach Spaces," International Journal of Applied Physics and Mathematics vol. 5, no. 2, pp. 115-125, 2015.

General Information

ISSN: 2010-362X
Frequency: Bimonthly (2011-2014); Quarterly (Since 2015)
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca
Abstracting/ Indexing: Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Electronic Journals Library, Engineering & Technology Digital Library, Nanowerk Database, Google Scholar and ProQuest
E-mail: ijapm@iap.org
  • Mar 11, 2016 News!

    IJAPM Vol.5, No.3 has been indexed by EI (Inspec).   [Click]

  • Sep 28, 2017 News!

    Vol 7, No 4 has been published with online version     [Click]

  • Aug 10, 2017 News!

    The papers published in Vol 7, No 3 have all received dois from Crossref

  • Jul 21, 2017 News!

    Vol 7, No 3 has been published with online version     [Click]

  • Feb 22, 2017 News!

    The papers published in Vol.7, No.2 have all received dois from Crossref.

  • Read more>>