Oscillation for higher order nonlinear delay differential equations

摘要

In this paper, we establish some oscillation criteria for n order non-linear delay differential equationx(n)(t)+∑i=1mpi(t)|x(t−τi)|αi−1x(t−τi)=0,t⩾t0,and the super-linear n order neutral delay differential equation[x(t)−px(t−τ)](n)+Q(t)|x(t−σ)|α−1x(t−σ)=0,t⩾t0,in the case ∑i=1mαi>m and α>1, respectively, where n⩾1 is an odd integer, Q,pi∈C([t0,∞),[0,∞)), τ,σ,τi>0.