Geodesic
Stable perturbations of linear differential equations generating a~uniformly bounded group
Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1246-1259

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Stability problems for solutions of the differential equation $u'(t)=Au+\varepsilon B(t,u)$ in a Banach space are considered. It is assumed that for $\varepsilon=0$ this equation generates a uniformly bounded group of class $C_0$. Sufficient conditions on $B$ and $A$ are found under which the solutions of this equation are bounded for small $\varepsilon$. A linearization principle is proved for this equation under certain conditions on the operator $B$. Bibliography: 9 titles.
Keywords: differential equations in a Banach space, stability of solutions. 
@article{SM_2017_208_8_a7,
     author = {V. V. Skazka},
     title = {Stable perturbations of linear differential equations generating a~uniformly bounded group},
     journal = {Sbornik. Mathematics},
     pages = {1246--1259},
     publisher = {mathdoc},
     volume = {208},
     number = {8},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_8_a7/}
}
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V. V. Skazka. Stable perturbations of linear differential equations generating a~uniformly bounded group. Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1246-1259. http://geodesic.mathdoc.fr/item/SM_2017_208_8_a7/