Hristova, S. G., M. B. Kapitanova, S. I. Kostadinov
Method of a small parameter for a class of nonautonomous systems of second order differential equations with impulses
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 50, 3-8 (1997)

MSC:

34A37 Differential equations with impulses

34E05 Asymptotic expansions

Abstract: Systems with impulses find a wide application to mathematical modelling in ratio engineering,
physics, chemistry, biology, etc. . The development of the qualitative
theory of these systems is of particular interest since there solutions
can be found in an explicit form only in exceptional cases.

An efficient method by means of which the periodic solutions of differential equations are investigated
successfully is the method of a small parameter. In the present paper by means
of this method a periodic solution of a nonautonomous system of second
order impulsive differential equations is constructed. The case when the characteristic
equation has some complex conjugate roots is studied.
Keywords: Differential equations with impulses, Asymptotic expansions