一类二阶微分方程的振动准则

Oscillate Criteria for a Kind of Second-order Differential Equations

对于二阶半线性中立型微分方程:(r(t)︱h′(t)︱^(α-1)h′(t))′+g(t)︱x(σ(t))︱^(α-1)x(σ(t))=0的振动性,本文在文[1]的基础上,利用广义Riccati变换、函数单调性和经典不等式,对其做了进一步研究,建立新准则改进了文献的结果,并提供了证明,并给出例子.

This paper considered oscillatory behavior of a class of second-order linear differential equation of the form (r(t)︱h′(t)︱^(α-1)h′(t))′+g(t)︱x(σ(t))︱^(α-1)x(σ(t))=0.Using ageneralized Riccati transform,classical inequality and functional monotonicity,we have made further study on it due to Ravi P et al.[1].A new oscillation criterion is established to amend the related results reported in the literature.We have proved the new oscillation criterion and an example is given.