Geodesic
Asymptotics of solutions of infinite-dimensional homogeneous dynamical systems
Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 115-126

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In this paper we study the connection between the uniform asymptotic stability and the power-law or exponential asymptotics of the solutions of infinite-dimensional systems (differential equations in Banach spaces, functional differential equations, and completely solvable multidimensional differential equations). 
@article{MZM_1998_63_1_a11,
     author = {D. N. Cheban},
     title = {Asymptotics of solutions of infinite-dimensional homogeneous dynamical systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {115--126},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a11/}
}
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D. N. Cheban. Asymptotics of solutions of infinite-dimensional homogeneous dynamical systems. Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 115-126. http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a11/