Geodesic
Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 260-268

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V. A. Trenogin's results on the stability of solutions to the Cauchy problem for differential equations in Banach spaces with respect to linear approximation in the case of degenerate linearization are presented from the viewpoint of branching equation in the root subspace. 
@article{TM_2012_278_a23,
     author = {V. A. Trenogin and B. V. Loginov and L. R. Kim-Tyan},
     title = {Stability of solutions to the {Cauchy} problem with respect to linear approximation, and branching equation in the root subspace},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {260--268},
     publisher = {mathdoc},
     volume = {278},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_278_a23/}
}
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V. A. Trenogin; B. V. Loginov; L. R. Kim-Tyan. Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 260-268. http://geodesic.mathdoc.fr/item/TM_2012_278_a23/