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Acta Mathematicae Applicatae Sinica

, Volume 5, Issue 4, pp 298–309 | Cite as

On a system of second order differential equations with periodic impulse coefficients

  • Qin Chaobin 
  • Qin Yuanxun 
Article

Abstract

A thorough investigation of the system
$$\frac{{d^2 y(x)}}{{dx^2 }} + p(x)y(x) = 0$$
with periodic impulse coefficients
$$\begin{gathered} p(x) = \left\{ {\begin{array}{*{20}c} {1, 0 \leqslant x< x_0 (2\pi > x_0 > 0)} \\ { - \eta , x_0 \leqslant x< 2\pi (\eta > 0)} \\ \end{array} } \right. \hfill \\ p(x) = p(x + 2\pi ), ---\infty< x< \infty \hfill \\ \end{gathered} $$
is given, and the method can be applied to one with other periodic impulse coefficients.

Keywords

Differential Equation Math Application Order Differential Equation Periodic Impulse Impulse Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    D. Willet, Classification of Second Order Linear Differential Equations with Respect to Oscillation,Advance in Mathematics,1 (1967), 594–623.Google Scholar
  2. [2]
    Pu Fuquan, A Special Kind of Nonoscillatory Second Order Linear Differential Equations,Acta Mathematicae Applicatas Sinica (English Series),4 (1988), 69–74.Google Scholar
  3. [3]
    E. Coddington and N. Levinson, Theory of Ordinary Differential Equation, N. Y., McGrew-Hill, 1955, 208–211.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1989

Authors and Affiliations

  • Qin Chaobin 
    • 1
  • Qin Yuanxun 
    • 2
  1. 1.Institute of Engineering ThermophysicsAcademia SinicaChina
  2. 2.Institute of Applied MathematicsAcademia SinicaChina

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