New Qualitative Results for Solutions of Functional Differential Equations of Second Order
In this paper, we are concerned with the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of nonlinear functional differential equations of second order by the s...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/3151742 |
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| _version_ | 1832565495074652160 |
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| author | Cemil Tunç Sultan Erdur |
| author_facet | Cemil Tunç Sultan Erdur |
| author_sort | Cemil Tunç |
| collection | DOAJ |
| description | In this paper, we are concerned with the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of nonlinear functional differential equations of second order by the second method of Lyapunov. We obtain sufficient conditions guaranteeing the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of the equations considered. We give an example for illustrations by MATLAB-Simulink, which shows the behaviors of the orbits. The findings of this paper extend and improve some results that can be found in the literature. |
| format | Article |
| id | doaj-art-29494c91270c44f8a4d617ed38bbd1f3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-29494c91270c44f8a4d617ed38bbd1f32025-02-03T01:07:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/31517423151742New Qualitative Results for Solutions of Functional Differential Equations of Second OrderCemil Tunç0Sultan Erdur1Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, 65080, Van, TurkeyDepartment of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, 65080, Van, TurkeyIn this paper, we are concerned with the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of nonlinear functional differential equations of second order by the second method of Lyapunov. We obtain sufficient conditions guaranteeing the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of the equations considered. We give an example for illustrations by MATLAB-Simulink, which shows the behaviors of the orbits. The findings of this paper extend and improve some results that can be found in the literature.http://dx.doi.org/10.1155/2018/3151742 |
| spellingShingle | Cemil Tunç Sultan Erdur New Qualitative Results for Solutions of Functional Differential Equations of Second Order Discrete Dynamics in Nature and Society |
| title | New Qualitative Results for Solutions of Functional Differential Equations of Second Order |
| title_full | New Qualitative Results for Solutions of Functional Differential Equations of Second Order |
| title_fullStr | New Qualitative Results for Solutions of Functional Differential Equations of Second Order |
| title_full_unstemmed | New Qualitative Results for Solutions of Functional Differential Equations of Second Order |
| title_short | New Qualitative Results for Solutions of Functional Differential Equations of Second Order |
| title_sort | new qualitative results for solutions of functional differential equations of second order |
| url | http://dx.doi.org/10.1155/2018/3151742 |
| work_keys_str_mv | AT cemiltunc newqualitativeresultsforsolutionsoffunctionaldifferentialequationsofsecondorder AT sultanerdur newqualitativeresultsforsolutionsoffunctionaldifferentialequationsofsecondorder |