Geodesic
Using an Analog of the Lyapunov Function with Sign-Alternating Derivative in the Study of Global Asymptotic Stability of Equilibria
Matematičeskie zametki, Tome 96 (2014) no. 2, pp. 212-216

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the problem of global asymptotic stability of the zero solution of a system of autonomous differential equations. A proposed method for studying this problem is based on the use of an auxiliary positive definite function whose derivative can be sign-alternating along solutions of the system.
Keywords: global asymptotic stability, stability, equilibrium, Lyapunov function. 
@article{MZM_2014_96_2_a5,
     author = {A. O. Ignatyev},
     title = {Using an {Analog} of the {Lyapunov} {Function} with {Sign-Alternating} {Derivative} in the {Study} of {Global} {Asymptotic} {Stability} of {Equilibria}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {212--216},
     publisher = {mathdoc},
     volume = {96},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_2_a5/}
}
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A. O. Ignatyev. Using an Analog of the Lyapunov Function with Sign-Alternating Derivative in the Study of Global Asymptotic Stability of Equilibria. Matematičeskie zametki, Tome 96 (2014) no. 2, pp. 212-216. http://geodesic.mathdoc.fr/item/MZM_2014_96_2_a5/