Kang Sheng-liang, Zhang An-jiang. Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval[J]. Applied Mathematics and Mechanics, 1987, 8(8): 669-688.
Citation: Kang Sheng-liang, Zhang An-jiang. Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval[J]. Applied Mathematics and Mechanics, 1987, 8(8): 669-688.

Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval

  • Received Date: 1986-06-06
  • Publish Date: 1987-08-15
  • In this paper we study initial value problems on the infinite interval: where x, f∈Em, y, g∈En,εare real small positive parameters,0≤t<+∞. On condition that gy(t) is nonsingular and under other assumptions, we have proved that there areserial (k+m*)-dimensionalmanifolds {SR(ε)}∈Em+n such that (1.1) degenerates regularly provided(ξ(ε),η(ε))∈SR(ε). Besides, the R-order asymptotic expansions of solutions are constructed, and their errors are estimated.
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