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Existence of Multiple Periodic Solutions for Cubic Nonautonomous Differential Equation
Joint Authors
Chu, Yu-Ming
Akram, Saima
Kalsoom, Humaira
Idrees, Muhammad
Nawaz, Allah
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-03
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
In this article, approaches to estimate the number of periodic solutions of ordinary differential equation are considered.
Conditions that allow determination of periodic solutions are discussed.
We investigated focal values for first-order differential nonautonomous equation by using the method of bifurcation analysis of periodic solutions from a fine focus Z=0.
Keeping in focus the second part of Hilbert’s sixteenth problem particularly, we are interested in detecting the maximum number of periodic solution into which a given solution can bifurcate under perturbation of the coefficients.
For some classes like C7,7,C8,5,C8,6,C8,7, eight periodic multiplicities have been observed.
The new formulas ξ10 and ϰ10 are constructed.
We used our new formulas to find the maximum multiplicity for class C9,2.
We have succeeded to determine the maximum multiplicity ten for class C9,2 which is the highest known multiplicity among the available literature to date.
Another challenge is to check the applicability of the methods discussed which is achieved by presenting some examples.
Overall, the results discussed are new, authentic, and novel in its domain of research.
American Psychological Association (APA)
Akram, Saima& Nawaz, Allah& Kalsoom, Humaira& Idrees, Muhammad& Chu, Yu-Ming. 2020. Existence of Multiple Periodic Solutions for Cubic Nonautonomous Differential Equation. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1200634
Modern Language Association (MLA)
Akram, Saima…[et al.]. Existence of Multiple Periodic Solutions for Cubic Nonautonomous Differential Equation. Mathematical Problems in Engineering No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1200634
American Medical Association (AMA)
Akram, Saima& Nawaz, Allah& Kalsoom, Humaira& Idrees, Muhammad& Chu, Yu-Ming. Existence of Multiple Periodic Solutions for Cubic Nonautonomous Differential Equation. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1200634
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1200634