Electron. J. Diff. Equ., Vol. 2011 (2011), No. 40, pp. 1-14.

Interval criteria for oscillation of second-order impulsive differential equation with mixed nonlinearities

Velu Muthulakshmi, Ethiraju Thandapani

Abstract:
We establish sufficient conditions for the oscillation of all solutions to the second-order impulsive differential equation
$$\displaylines{ \big(r(t)x'(t)\big)'+p(t)x'(t)+q(t)x(t)+\sum_{i=1}^n q_i(t)|x(t)|^{\alpha_i}\hbox{sgn} x(t)=e(t),\quad t\neq \tau_k,\cr x({\tau_k}^+)=a_k x({\tau_k}),\quad x'({\tau_k}^+)=b_k x'({\tau_k}). }$$
The results obtained in this paper extend some of the existing results and are illustrated by examples.

Submitted October 6, 2010. Published March 9, 2011.
Math Subject Classifications: 34C10, 34A37
Key Words: Oscillation; second order; impulse; damping term; mixed nonlinearities.

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Velu Muthulakshmi
Department of Mathematics, Periyar University
Salem-636 011, India
email: vmuthupu@gmail.com
Ethiraju Thandapanii
Ramanujan Institute for Advanced Study in Mathematics
University of Madras, Chennai-600005, India
email: ethandapani@yahoo.co.in

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