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Monotone iterative technique for the initial value problem for differential equations with non-instantaneous impulses

Author

Listed:
  • Agarwal, Ravi
  • O'Regan, D.
  • Hristova, S.

Abstract

An algorithm for constructing two monotone sequences of upper and lower solutions of the initial value problem for a scalar nonnlinear differential equation with non-instantaneous impulses is given. The impulses start abruptly at some points and their action continue on given finite intervals. We prove that the functional sequences are convergent and their limits are minimal and maximal solutions of the considered problem. An example is given to illustrate the results.

Suggested Citation

  • Agarwal, Ravi & O'Regan, D. & Hristova, S., 2017. "Monotone iterative technique for the initial value problem for differential equations with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 45-56.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:45-56
    DOI: 10.1016/j.amc.2016.10.009
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    Cited by:

    1. Surang Sitho & Chayapat Sudprasert & Sotiris K. Ntouyas & Jessada Tariboon, 2020. "Noninstantaneous Impulsive Fractional Quantum Hahn Integro-Difference Boundary Value Problems," Mathematics, MDPI, vol. 8(5), pages 1-15, April.
    2. JinRong Wang & Michal Fečkan & Amar Debbouche, 2019. "Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 573-587, August.
    3. Amit K Verma & Biswajit Pandit & Ravi P. Agarwal, 2021. "Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth," Mathematics, MDPI, vol. 9(7), pages 1-25, April.

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