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Stability of solutions of certain third order non-autonomous ordinary differential equations

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Abstract

Sufficient criteria were established to ensure the stability of solutions of certain third order nonlinear non-autonomous ordinary differential equations of the form

$$\begin{aligned} {\mathop {x}\limits ^{...}}+(a(t,x,\dot{x},\ddot{x})+m(t,x,\dot{x},\ddot{x})) \ddot{x}+b(t)\phi (x,\dot{x})+c(t,x,\dot{x},\ddot{x})h(x)= p(t,x,\dot{x},\ddot{x}). \end{aligned}$$

By using Lyapunov’s direct method, we obtained new result on the subject being considered. An example is hereby introduced to illustrate the importance of the result obtained with graphical representation.

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Acknowledgements

The authors will like to thank the anonymous referee whose useful comments and contributions have greatly improved on the original manuscript.

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  1. Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

    D. O. Adams & M. O. Omeike

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  1. D. O. Adams
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  2. M. O. Omeike
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Correspondence to D. O. Adams.

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Adams, D.O., Omeike, M.O. Stability of solutions of certain third order non-autonomous ordinary differential equations. Afr. Mat. 32, 131–138 (2021). https://doi.org/10.1007/s13370-020-00815-z

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