Geodesic
Lagrangian asymptotic behaviour of solutions of inhomogeneous systems
Sbornik. Mathematics, Tome 197 (2006) no. 9, pp. 1341-1351

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The problem under consideration concerns when a system of ordinary differential equations reducible to a weakly non-linear system has solutions with the same asymptotic behaviour as solutions of the corresponding homogeneous system. The existence and uniqueness of global solutions to the inhomogeneous system is established in the form of a solution to a homogeneous system of differential equations, in the case when asymptotic initial data is prescribed at the singular points of these systems. Bibliography: 6 titles. 
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     author = {L. D. Kudryavtsev},
     title = {Lagrangian asymptotic behaviour  of solutions of inhomogeneous systems},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {197},
     number = {9},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_9_a4/}
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L. D. Kudryavtsev. Lagrangian asymptotic behaviour  of solutions of inhomogeneous systems. Sbornik. Mathematics, Tome 197 (2006) no. 9, pp. 1341-1351. http://geodesic.mathdoc.fr/item/SM_2006_197_9_a4/