Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary

Abdelkader Moumen, Amin Benaissa Cherif, Mohamed Ferhat, Mohamed Bouye and Khaled Zennir ()
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Abdelkader Moumen: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Amin Benaissa Cherif: Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, P.O. Box 1505, Bir El Djir 31000, Oran, Algeria
Mohamed Ferhat: Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, P.O. Box 1505, Bir El Djir 31000, Oran, Algeria
Mohamed Bouye: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Khaled Zennir: Department of Mathematics, College of Sciences and Arts in Ar-Rass, Qassim University, Saudi Arabia

Mathematics, 2023, vol. 11, issue 24, 1-17

Abstract: A class for systems of nonlinear second-order differential equations with periodic impulse action are considered. An urgent problem for this class of differential equations is the problem of the quantitative study (existence) in the case when the phase space of the equation is, in the general case, some Banach space. In this work, sufficient conditions for the existence of solutions for a system with parameters are obtained. The results are obtained by using fixed point theorems for operators on a cone. Our approach is based on Schaefer’s fixed point theorem more precisely. In addition, the existence of positive solutions is also investigated.

Keywords: iterative methods; periodic solutions; impulses; matrix convergent to 0; generalized banach space; Schaefer’s fixed point theorem; differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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