Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary
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,...
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/24/4907 |
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| author | Abdelkader Moumen Amin Benaissa Cherif Mohamed Ferhat Mohamed Bouye Khaled Zennir |
| author_facet | Abdelkader Moumen Amin Benaissa Cherif Mohamed Ferhat Mohamed Bouye Khaled Zennir |
| author_sort | Abdelkader Moumen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T20:34:01Z |
| format | Article |
| id | doaj.art-9ab61dfd8b4148b888040419b5a6e7f8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T20:34:01Z |
| publishDate | 2023-12-01 |
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| series | Mathematics |
| spelling | doaj.art-9ab61dfd8b4148b888040419b5a6e7f82023-12-22T14:23:15ZengMDPI AGMathematics2227-73902023-12-011124490710.3390/math11244907Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic BoundaryAbdelkader Moumen0Amin Benaissa Cherif1Mohamed Ferhat2Mohamed Bouye3Khaled Zennir4Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi ArabiaDepartment 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, AlgeriaDepartment 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, AlgeriaDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts in Ar-Rass, Qassim University, Saudi ArabiaA 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.https://www.mdpi.com/2227-7390/11/24/4907iterative methodsperiodic solutionsimpulsesmatrix convergent to 0generalized banach spaceSchaefer’s fixed point theorem |
| spellingShingle | Abdelkader Moumen Amin Benaissa Cherif Mohamed Ferhat Mohamed Bouye Khaled Zennir Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary Mathematics iterative methods periodic solutions impulses matrix convergent to 0 generalized banach space Schaefer’s fixed point theorem |
| title | Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary |
| title_full | Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary |
| title_fullStr | Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary |
| title_full_unstemmed | Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary |
| title_short | Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary |
| title_sort | existence results for systems of nonlinear second order and impulsive differential equations with periodic boundary |
| topic | iterative methods periodic solutions impulses matrix convergent to 0 generalized banach space Schaefer’s fixed point theorem |
| url | https://www.mdpi.com/2227-7390/11/24/4907 |
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