Abstract—The importance of differential equations in scientific world is a crystal-clear fact. Many problems in physics, ecology, biology, engineering etc. can be modeled by ordinary differential equations and very few of them can be solved in terms of elementary functions. However, it is possible to reveal the main features of the solutions by the help of qualitative methods. In this study, we try to show that the conditions for some nonlinear equations to be asymptotically stable.

Index Terms—Liapunov's second method, ordinary differential equations, stability analysis.

The authors are with Celal Bayar University, Faculty of Arts and Science, Department of Mathematics, Muradiye Campus, 45030, Manisa, Turkey (email: necdet.bildik@cbu.edu.tr).

Cite: Necdet Bildik, Sinan Deniz, "On the Asymptotic Stability of Some Particular Differential Equations," International Journal of Applied Physics and Mathematics vol. 5, no. 4, pp. 252-258, 2015.