Some new qualitative results for two dimensional nonlinear differential systems | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 13, Issue 1, 2025, Pages 1-13 PDF (523.86 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2024.332843.1286 | ||
| Author | ||
| Melek Gözen* | ||
| Department of Business Administration Faculty of Management Van Yuzuncu Yil University 65080, Erci\c{s}–Van, Turkey | ||
| Abstract | ||
| As we know ordinary differential equations, systems of ordinary differential equations, in particular, two dimensional nonlinear differential systems have significant and various applications in qualitative theory of ordinary differential equations. In some real world applications, it is needed to have information in relation to the qualitative concepts called stability, boundedness, convergence, etc. of solutions of that kind of mathematical models. Most of time, exact solutions of that kind of equations cannot be obtained explicitly, except numerically. In the pertinent literature, one of the famous method is known the Lyapunov’s second method, which allows to have information about qualitative behaviors of solutions without solving the equation understudy. In this study, we deal with a nonlinear a two dimensional nonlinear differential system. We examine uniform asymptotic stability, boundedness, uniform boundedness and uniform-ultimate boundedness of solutions of that two dimensional nonlinear differential system. We will prove three new theorems on the mentioned qualitative concepts by using the Lyapunov’s second method. We provide two examples to demonstrate how the results of the study can be applied. The results of this study generalize some recent results, which can be found in the present literature. | ||
| Keywords | ||
| Differential system; two dimensional; stability; boundedness; second method of Lyapunov | ||
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