Asymptotic integration of functional differential systems with oscillatory decreasing coefficients: a center manifold approach

作者：Nesterov Pavel^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2016, (33): 1-43.

DOI：10.14232/ejqtde.2016.1.33

• asymptotic integration
• functional differential systems
• center manifold
• method of averaging
• Levinson's theorem
• oscillatory decreasing coefficients

In this paper we study the asymptotic integration problem in the neighborhood of infinity for a certain class of linear functional differential systems. We propose a method for the construction of the asymptotics of solutions in the critical case. Using the ideas of the center manifold theory we show the existence of the so called critical manifold that is positively invariant for trajectories of the initial system. We establish that the dynamics of solutions lying on this manifold defines the asymptotics for all solutions. We illustrate the proposed method with an example of the construction of the asymptotics for solutions of a certain scalar delay differential equation.

• 出版日期2016