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On Positivity of Solutions of Delayed Differential Equation with State Dependent Impulses

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Parallel Processing and Applied Mathematics (PPAM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2328))

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Abstract

We consider the delay differential equation

with state dependent impulses. We give sufficient conditions for positivity of solutions of the Cauchy and periodic problems as well as conditions for positivity of solutions of the initial problem with a condition on the right end of the interval [0, ω]. We also formulate sufficient conditions for nonoscillation of solutions of the homogeneous equation (f = 0, ϕ = 0) on the halfline.

The research has been supported by Kamea and Giladi programs of the Ministry of Absorption of the State of Israel

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References

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Author information

Authors and Affiliations

  1. The Research Institute, The College of Judea and Samaria, 44837, Ariel, Israel

    Alexander Domoshnitsky & Michael Drakhlin

  2. Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Elena Litsyn

Authors
  1. Alexander Domoshnitsky
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  2. Michael Drakhlin
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  3. Elena Litsyn
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Technical University of Czestochowa, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Roman Wyrzykowski

  2. Computer Science Department, University of Tennessee, 122 Volunteer Blvd, Knoxville, TN, 37996-3450, USA

    Jack Dongarra

  3. Computer Science Department, Oklahoma State University, 700 N. Greenwood Ave., Tulsa, OK, 74106, USA

    Marcin Paprzycki

  4. DTU, UNI-C, Danish Computing Centre for Research and Education, Bldg. 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2002 Springer-Verlag Berlin Heidelberg

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Domoshnitsky, A., Drakhlin, M., Litsyn, E. (2002). On Positivity of Solutions of Delayed Differential Equation with State Dependent Impulses. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_97

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  • DOI: https://doi.org/10.1007/3-540-48086-2_97

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43792-5

  • Online ISBN: 978-3-540-48086-0

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