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Open AccessArticle

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

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Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, Algeria
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Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China
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Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1134; https://doi.org/10.3390/math7121134
Received: 18 August 2019 / Revised: 11 November 2019 / Accepted: 12 November 2019 / Published: 20 November 2019
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. View Full-Text
Keywords: second order differential equations; mild solution; non-instantaneous impulses; Kuratowski measure of noncompactness; Darbo fixed point second order differential equations; mild solution; non-instantaneous impulses; Kuratowski measure of noncompactness; Darbo fixed point
MDPI and ACS Style

Benchohra, M.; Rezoug, N.; Samet, B.; Zhou, Y. Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses. Mathematics 2019, 7, 1134.

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