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

Mouffak Benchohra, Noreddine Rezoug, Bessem Samet and Yong Zhou
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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
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

Mathematics, 2019, vol. 7, issue 12, 1-20

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.

Keywords: second order differential equations; mild solution; non-instantaneous impulses; Kuratowski measure of noncompactness; Darbo fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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