Geodesic
Center manifold method in the asymptotic integration problem for functional differential equations with oscillatory decreasing coeffcients.~II
Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 5, pp. 5-37

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In this paper we study the asymptotic integration problem in the neighborhood of infnity for a certain class of linear functional differential systems. We construct the asymptotics for the solutions of the considered systems in a critical case. In the second part of the work we establish the existence of a critical manifold for the considered class of systems and study its main properties. We also investigate the asymptotic integration problem for a reduced system. We illustrate the proposed method with an example of constructing the asymptotics for the solutions of a certain scalar delay differential equation.
Keywords: functional-differential equations, critical manifold, asymptotic integration, averaging method, Levinson's theorem. 
@article{MAIS_2014_21_5_a0,
     author = {P. N. Nesterov},
     title = {Center manifold method in the asymptotic integration problem for functional differential equations with oscillatory decreasing {coeffcients.~II}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {5--37},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a0/}
}
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P. N. Nesterov. Center manifold method in the asymptotic integration problem for functional differential equations with oscillatory decreasing coeffcients.~II. Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 5, pp. 5-37. http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a0/