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

Abstract

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

Keywords

• Oscillation
• second order
• impulse
• damping term
• mixed nonlinearities