Geodesic
On the Lyapunov type inequality
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 21-29

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A.M. Lyapunov proved the inequality that makes it possible to estimate the distance between two consecutive zeros $ a $ and $ b $ of solutions of a linear differential equation of the second order $ x''(t) + q (t) x (t) = 0$ where $ q (t) $ is a continuous function for $ t \in [a, b] $. In the present note, a similar problem is solved for a linear differential equation of the form $ x'' (t) + p (t) x'(t) + q (t) x (t) = 0 $. The obtained inequality is applied to the periods estimate of periodic solutions of nonlinear differential Liénard and Van der Pol equations.
Keywords: Lyapunov–type inequality
Mots-clés : Liénard equation, van der Pol equation. 
@article{IVM_2020_6_a3,
     author = {A. O. Ignatyev},
     title = {On the {Lyapunov} type inequality},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {21--29},
     publisher = {mathdoc},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_6_a3/}
}
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A. O. Ignatyev. On the Lyapunov type inequality. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 21-29. http://geodesic.mathdoc.fr/item/IVM_2020_6_a3/