广义Emden-Fowler微分方程的振动准则(英文)

Oscillation Criteria for Generalized Emden-Fowler Equation

本文运用广义Riccati变换和中值定理,讨论了广义Emden-Fowler方程(r(t)|z'(t)|^(α-1)z'(t))'+q(t)|x(σ(t))|^(β-1)x(σ(t))=0的振动性,其中z(t)=x(t)+p(t)x(τ(t)),β≥α>0,得到了该方程存在振动解的充分条件,推广和改进了已有结果,并用实例给出了其应用.

In this paper, we consider the new generalized Emden-Fowler equation with neutral type delays:(r(t)|z'(t)|^(α-1)z'(t))'+q(t)|x(σ(t))|^(β-1)x(σ(t)) =0, where z(t)=x(t)+p(t)x(τ(t)), β≥α>0. By employing the generalized Riccati transformation technique and the mean value theorem, some sufficient conditions which guarantee that every solution oscillates are established, which have extended the results in the cited literature. Examples are provided to illustrate the significance of our results.