Geodesic
Approximate solution of a~boundary value problem for the Lyapunov differential equation with a~parameter
Sibirskij žurnal industrialʹnoj matematiki, Tome 9 (2006) no. 2, pp. 107-115

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A special boundary value problem is studied for the Lyapunov differential equation which is used for investigation of the asymptotic properties of solutions to systems of periodic differential equations with a parameter. An algorithm is proposed for constructing an approximate solution to this boundary value problem, and conditions on the parameter are found under which the zero solution to the system is asymptotically stable. 
@article{SJIM_2006_9_2_a9,
     author = {I. I. Matveeva and E. A. Samuilova},
     title = {Approximate solution of a~boundary value problem for the {Lyapunov} differential equation with a~parameter},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {107--115},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2006_9_2_a9/}
}
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I. I. Matveeva; E. A. Samuilova. Approximate solution of a~boundary value problem for the Lyapunov differential equation with a~parameter. Sibirskij žurnal industrialʹnoj matematiki, Tome 9 (2006) no. 2, pp. 107-115. http://geodesic.mathdoc.fr/item/SJIM_2006_9_2_a9/