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Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses

Author

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  • Mouffak Benchohra

    (Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, Algeria
    Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Noreddine Rezoug

    (Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, Algeria)

  • Bessem Samet

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Yong Zhou

    (Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China
    Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China)

Abstract

We consider a non-instantaneous system represented by a second order nonlinear differential equation in a Banach space E . We use the family of linear bounded operators introduced by Kozak, Darbo fixed point method and Kuratowski measure of noncompactness. A new set of sufficient conditions is formulated which guarantees the existence of the solution of the non-instantaneous system. An example is also discussed to illustrate the efficiency of the obtained results.

Suggested Citation

  • Mouffak Benchohra & Noreddine Rezoug & Bessem Samet & Yong Zhou, 2019. "Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses," Mathematics, MDPI, vol. 7(12), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1134-:d:289082
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    References listed on IDEAS

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    1. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
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    Cited by:

    1. Martina Pavlačková & Valentina Taddei, 2022. "Mild Solutions of Second-Order Semilinear Impulsive Differential Inclusions in Banach Spaces," Mathematics, MDPI, vol. 10(4), pages 1-25, February.

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