Oscillation and asymptotic analysis on a new generalized Emden–Fowler equation

摘要

In this work, we analyze the new generalized Emden–Fowler equation with neutral type delays:r(t)|Z′(t)|α-1Z′(t)′+q(t)|x(σ(t))|β-1x(σ(t))=0,where Z(t)=x(t)+p(t)x(τ(t)),α⩾β>0. By use of averaging technique and specific analytical skills, some easily-accessible oscillation and asymptotic criteria are established, which have extended the results in the cited literature.