Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 40, pp. 1-14.
Title: Interval criteria for oscillation of second-order impulsive
differential equation with mixed nonlinearities
Authors: Velu Muthulakshmi (Periyar Univ., Salem, India)
Ethiraju Thandapani (Univ. of Madras, Chennai, India)
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 09, 2011.
Math Subject Classifications: 34C10, 34A37
Key Words: Oscillation; second order; impulse; damping term;
mixed nonlinearities.