二阶非线性振动的Philos型积分平均

Integral Average of Philos Type for Second Order Nonlinear Oscillation

研究二阶非线性微分方程(a(t)x′(t))′+p(t)x′(t)+q(t)f(x(t))=0(E)的振动性,在较一般的假设下给出了若干新的振动准则.该文的方法不同于先前的作者[1-4,8-10,13-15],其结果推广和补充了Philos和Rogvchenko早先的结果.文中也给出了一个说出结果应用的例子.

The purpose of this paper is to study the oscillation of second order nonlinear differential equation （a（t）x′（t））′＋p（t）x′（t）＋q（t）x（t） = 0.（E） Some new oscillation criteria are established under quite general assumptions.Our methodology is somewhat different from that of previous authors[1-4,8-10,13-15].Our results extend and complement some earlier results of Philos and Rogovchenko.An example is also given to illustrate the results.