一类高阶非线性泛函方程的振动准则

Oscillation Criteria for a Class of Higher Order Nonlinear Functional Equations

研究了变系数高阶非线性泛函方程x(g(t))=P(t)x(t)+sum( )from i=1 to m Qi(t)x(gK+i(t))的解的振动性,得到了一些新的振动准则.所得结论推广了目前已有结果,此外,给出了新振动准则在差分方程中的一些应用.

This paper studies the oscillation of the solutions of high order nonlinear functional equation with variable coefficientsx（g（t））=P（t）x（t）＋ m∑im1 Qi（t）x（gK＋i（t））and some new oscillation criteria are obtained. The researches in this paper extend or improve some existent results at present. Some applications of differential equation are given.