具有非单调项的二阶微分方程的振动准则

主要利用降阶法,得到具有非单调项的二阶微分方程振动的充分条件.首先根据降阶法及相关的不等式知识,将带有非单调项的二阶微分方程转变为一阶微分方程.之后运用具有非单调项的一阶微分方程已知的相关结果,得到了二阶微分方程的振动准则,改进了以往的二阶微分方程解的振动结果.最后通过例题说明所得结论的可应用性.

Iterative oscillation tests for second-order differential equations with several non-monotone arguments

Sufficient oscillation conditions are obtained for second order differential equations with several non-monotone deviating arguments. The oscillation results are mainly based on the technique of reduction of order. First of all, the second order differential equations with non-monotonic terms are transformed into first order differential equations by means of the technique of reduction of order and related inequality knowledge. Then using the correlation known results of first order differential equations with non-monotonic terms, we obtain the oscillation criterion of second order differential equations with several non-monotone deviating arguments. And the oscillation criterion of the solutions of second order differential equations are improved. At last, some examples are given to illustrate the versatility of our results.