非线性中立型时滞微分方程解的零点距估计

Distribution ofzeros of solutions of the nonlinear neutral differential equations

泛函微分方程振动解的零点分布作为方程振动理论的一个重要分支,使方程振动解的研究更加定量化,但目前对非线性及多个变时滞微分方程振动解零点距估计的研究成果还很少.本文通过非线性问题线性化处理,多个变时滞取上下界的方法,对一类一阶非线性多个变时滞中立型微分方程振动解的零点距进行了估计,获得了方程所有解都振动的充分条件,改进和推广了已有的一些的结果.

The distribution of zeros of the oscillatory solutions of functional differential equations is an important branch of the oscillation theory. It makes the character of the oscillatory solutions more quantitative. Nowadays, studies are rare on the zeros estimation of the oscillatory solutions of nonlinear differential equations with variable delays. This paper discusses the distribu- tion of zeros of solution of the first order nonlinear neutral differential equation with variable delays by linearizing nonlinear problems and fixing the upper and lower bound of variable delays. Some sufficient conditions are obtained of oscillation ibr all solutions of the equation. Some known results are generalized and improved.