On the oscillation of impulsively damped halflinear oscillators

J. Karsai, University of Szeged, Szeged, Hungary
J. R. Graef, The University of Tennessee at Chattanooga

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 14. (2000), pp. 1-12.

Abstract: The authors consider the nonlinear impulsive system
$$(\phi_\beta(x'))' + \phi_\beta (x) = 0 \quad (t \neq t_n), \quad x'(t_n + 0) = b_n x' (t_n)$$
where $n = 1, 2 \dots $, $\phi_\beta(u)=|u|^\beta\sign u$ with $\beta>0$, and $0\le b_n \le 1$. They investigate the oscillatory behavior of the solutions. In the special case where $b_n=b<1$ and $t_{n}=t_0+n \,d,$ they give necessary and sufficient conditions for the oscillation of all solutions.

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