一类非单调二阶非线性泛函微分方程的振动判据

利用广义Riccati技巧和平均方法讨论了一类二阶非线性泛函微分方程,得到此类方程所有解振动的新准则.其中,这些振动准则在一定程度上与以往的结果均不同,它们仅依赖于半直线t0,∞)上的一列子区间的信息,而不是整条半直线t0,∞).特别地,给出了大量的振动解存在性结论,同时能够解决已有的结果不能处理的问题.

Oscillation criteria for a class of second order functional differential equations with nonmonotonous nonlinearity

This paper discusses a class of second order nonlinear functional differential equations.By using the generalized Riccati technique and the averaging technique,new oscillation criteria are obtained for all solutions of the equation to be oscillatory.Some of results in this paper are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of ,rather than on the whole half-line. In particular,our results complement a number of existing results and handle the case which is not covered by known criteria.