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

On a system of second order differential equations with periodic impulse coefficients 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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

, Volume 5 (4) – Jul 13, 2005
12 pages      /lp/springer-journals/on-a-system-of-second-order-differential-equations-with-periodic-ANbnRNjUEN
Publisher
Springer Journals
Copyright © 1989 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02005952
Publisher site
See Article on Publisher Site

### 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.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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