Mathematical systems theory

, Volume 9, Issue 3, pp 308–314 | Cite as

Asymptotic equilibrium of ordinary differential systems in a Banach space

  • A. Richard Mitchell
  • Roger W. Mitchell
Article
  • 49 Downloads

Abstract

The asymptotic equilibrium of differential systems in Euclidean spaces has been considered by several authors. These papers deal with a majorant function,g(t, u), which is either non-decreasing or non-increasing inu for eacht. In extending these results to differential systems in a Banach space additional conditions must be placed on the system. In this paper the Kuratowski measure of non-compactness is used to give conditions yielding asymptotic equilibrium of the system in a Banach space.

Keywords

Banach Space Computational Mathematic Euclidean Space Additional Condition Differential System 

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References

  1. [1]
    F. Brauer, Global behavior of solutions of ordinary differential equations,J. Math. Appl. 2 (1961), pp. 145–158.Google Scholar
  2. [2]
    K. Kuratowski,Topology, Vol. II, Academic Press, New York, 1962.Google Scholar
  3. [3]
    G. Ladas andV. Lakshmikantham, Asymptotic equilibrium of ordinary differential systems,J. Applicable Anal. (to appear).Google Scholar
  4. [4]
    G. Ladas andV. Lakshmikantham,Differential Equations in Abstract Spaces, Academic Press, New York, 1972.Google Scholar
  5. [5]
    G. Ladas andV. Lakshmikantham, Global existence and asymptotic equilibrium in banach spaces,J. Indian Math. Soc. 36 (1972), pp. 33–40.Google Scholar
  6. [6]
    V. Lakshmikantham andS. Leela,Differential and Integral Inequalities Theory and Application, Vol. I, Academic Press, New York, 1969.Google Scholar
  7. [7]
    Tien Yien Li,Existence of Solutions for Ordinary Differential Equations in Banach Spaces (to appear).Google Scholar
  8. [8]
    H. L. Royden,Real Analysis, MacMillan, New York, 1963.Google Scholar

Copyright information

© Swets & Zeitlinger B.V. 1975

Authors and Affiliations

  • A. Richard Mitchell
    • 1
  • Roger W. Mitchell
    • 1
  1. 1.Department of MathematicsThe University of Texas at ArlingtonArlingtonUSA

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