Geodesic
On the stability of the trivial solution to a periodic system of ordinary differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 3-11

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In this paper, we examine a normal system of ordinary differential equations whose right-hand side is periodic in the independent variable and locally smoothly depends on the small parameter and the phase variable. Using the properties of nonlinear approximations of the right and left monodromy operators, we prove conditions that guarantee the arbitrary smallness of perturbed solutions for sufficiently small initial values of the solutions and the parameter.
Keywords: differential equation, small parameter, stability, monodromy operator. 
@article{INTO_2022_216_a0,
     author = {V. V. Abramov},
     title = {On the stability of the trivial solution to a periodic system of ordinary differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--11},
     publisher = {mathdoc},
     volume = {216},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_216_a0/}
}
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V. V. Abramov. On the stability of the trivial solution to a periodic system of ordinary differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 3-11. http://geodesic.mathdoc.fr/item/INTO_2022_216_a0/