Geodesic
An analog of Kamenkov's critical case for systems of ordinary differential equations with pulse action
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 22-33

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We propose a new approach to studying the stability of systems of nonlinear differential equations with pulse action in critical cases. This approach rests on Lyapunov functions. We obtain sufficient conditions for the asymptotic stability of critical equilibria in some case analogous to Kamenkov's critical case.
Keywords: stability in the sense of Lyapunov, Kamenkov's critical case, differential equations with pulse action, Lyapunov's direct method. 
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     author = {A. I. Dvirnyǐ and V. I. Slyn'ko},
     title = {An analog of {Kamenkov's} critical case for systems of ordinary differential equations with pulse action},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {22--33},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a2/}
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A. I. Dvirnyǐ; V. I. Slyn'ko. An analog of Kamenkov's critical case for systems of ordinary differential equations with pulse action. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 22-33. http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a2/