Geodesic
Asymptotics of Solutions to Differential Equations near Singular Points
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 194-217

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Conditions are obtained under which all solutions to a normal system of equations asymptotically or strongly asymptotically approximate to polynomials as the argument tends to infinity. For the system of the form $L\mathbf x=\mathbf f$, where $L$ is a first-order linear differential operator, conditions are found under which all its solutions $L$-asymptotically approximate to the solutions of the homogeneous system $L\mathbf x=\mathbf 0$ as the argument tends to the singular point of the former system. 
@article{TM_2001_232_a16,
     author = {L. D. Kudryavtsev},
     title = {Asymptotics of {Solutions} to {Differential} {Equations} near {Singular} {Points}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {194--217},
     publisher = {mathdoc},
     volume = {232},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_232_a16/}
}
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L. D. Kudryavtsev. Asymptotics of Solutions to Differential Equations near Singular Points. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 194-217. http://geodesic.mathdoc.fr/item/TM_2001_232_a16/