International Journal of Mathematics Trends and Technology
Volume 69 | Issue 8 | Year 2023 | Article Id. IJMTT-V69I8P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I8P503
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 08 Jun 2023 | 24 Jul 2023 | 07 Aug 2023 | 24 Aug 2023 |
In this paper, we consider a class of one-dimensional nonautonomous differential equation. Under certain conditions, we construct the general solution and prove that the zero solution x = 0 are unstable. The differential equations of mechanics arises from the variational problems of the laws of nature, thus, the study about stability or the unstability of the special solutions, such as the zero solution, attracts many researchers. The novelty of this paper is that the system we consider is nonautonimous with the vector field being the polynomial of any order and prove that the zero solution is unstable. Our result will throw light on the research of the dynamics of celestial mechanics and enrich the differential equation theory.
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Yaxin Guo, "Unstability of Zero Solution of a Class Nonautonomous Differential Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 8, pp. 25-29, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I8P503
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