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Fourth Mississippi State Conference on Differential Equations and Computational Simulations
May 21-22, 1999
Mississippi State University and Electronic Journal of Differential Equations
Starkville, MS, USA |
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Organizers
Ratnasingham Shivaji, Bharat Soni, Jianping Zhu (Program Chair)
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On the asymptotic behavior of nonlinear systems with impulses
by
János Karsai
A. Szent-Györgyi Medical University, Hungary
Coauthors: John R. Graef
In the paper, we present results on the asymptotic behavior of solutions
of the nonlinear second order system
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(g(x'))'+ f(x) = 0, (t =/= tn); |
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g(x'(tn + 0)) = bn h ( g(x'(tn))), ( tn \nearrow \infty, as n --> \infty), |
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where f, g, h in C, and uf(u) > 0 and ug(u) > 0 for u =/= 0.
In the special case f(u) = g(u) = |u\alpha| sign u (0 < \alpha) and
h(u) = u, the system is called half-linear, which exhibits similar
behavior to the linear case. The analogous half-linear differential
equation with intermittent damping
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(f(x'))'+ a(t)x'+ f(x) = 0, |
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has been investigated by many authors.
Date received: May 4, 1999
Copyright © 1999 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cacr-85.