Differential Equations and Computational Simulations III

Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 97-108.

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On properties of nonlinear second order systems under
nonlinear impulse perturbations

John R. Graef & Janos Karsai

**Abstract:**

In this paper, we consider the impulsive second order system

where
.
In a previous paper, the authors proved that if
is strictly nonlinear, then this system has
infinitely many periodic solutions.
The impulses account for the main differences in the attractivity properties
of the zero solution. Here, we prove that these periodic
solutions are attractive in some sense, and we give good estimates for
the attractivity region.
Published November 12, 1998.

Mathematics Subject Classifications: 34D05, 34D20, 34C15.

Key words and phrases: Asymptotic stability, attractrivity of periodic
solutions, impulsive systems, nonlinear equations, second order systems.

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John R. Graef

Department of Mathematics and Statistics,
Mississippi State University

Mississippi State, MS 39762 USA.

Email address: graef@math.msstate.edu
Janos Karsai

Department of Medical Informatics,
Albert Szent-Gyorgyi Medical University

Szeged, Koranyi fasor 9, Hungary

Email address: karsai@silver.szote.u-szeged.hu

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