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 


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.


Differential Equation Math Application Order Differential Equation Periodic Impulse Impulse Coefficient 
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  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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