半线性中立型Emden-Fowler泛函微分方程的振动准则

Oscillation criteria for a certain half-linear Emden-Fowler functional differential equations of neutral type

建立了中立型Emden-Fowler泛函微分方程(r(t)︱z′(t)︱^(α-1)z′(t))′+q(t)︱x(σ(t))︱^(β-1)x(σ(t))=0,t≥t_0的若干振动准则,推广、统一了半线性微分方程和Emden-Fowler型微分方程的某些振动性结果,其中z(t)=x(t)+p(t)x(τ(t)),α>0,β>0为常数.最后,通过几个实例说明了结果的正确性.

Some new oscillation criteria are established for the hal＆linear Emden-Fowler functionaldifferential equations of neutral type of the form （r（t）z′（t）α-1 z′（t））′＋q（t）x（σ（t））β-1 x（σ（t））=0,t≥t0,wherez（t）=x（t）＋p（t）x（τ（t））,α〉0,β〉0. Our results generalize and unify some known results on half-linear differential equations and Emden-Fowlerprovided to show the importance of our results.type equations. Several illustrating examples are also