一类二阶Emden-Fowler型微分方程的若干振动条件

New oscillatory conditions of a class of the second-order Emden-Fowler differential equations

利用Riccati变换技术,借助Bernoulli不等式和Yang不等式以及数学分析技巧,研究了具有非线性中立项的二阶广义Emden-Fowler型微分方程的振动性,考虑非正则情形■,建立了该方程的若干振动准则。最后用2个例子说明,这些准则推广并改进了一些已有的结果,且具有较好的实用性和可操作性。

We investigate the oscillatory behavior of a class of the second-order generalized Emden-Fowler-type differential equations with a nonlinear neutral term the concerned equation is in a noncanonical form,i.e.∫^+∞/t0 a^-1/β(t)dt<+∞.By using the generalized Riccatitransformation,Bernoulliinequality,Yang inequality and t0 integral averaging technique,we establish some new oscillation criterions for the equations.Two illustrative examples are provided to show that our results extend and improve those reported in the literature,and have practicability and maneuverability.