一类偶数阶非线性中立型偏微分方程组的振动判据

Oscillation criteria of systems of certain even order nonlinear neutral partial differential equations

讨论一类偶数阶非线性中立型偏微分方程组的振动性,利用Green公式和边值条件将这类非线性中立型偏微分方程组的振动问题转化为中立型微分不等式不存在最终正解的问题,并利用最终正解的定义和微分不等式方法,获得了该类方程组在两类不同边值条件下所有解振动的若干充分性条件。所得结果为解决物理学、生物学、工程学等学科领域中的实际问题提供了数学理论基础。

The oscillation of solutions to the systems of certain even order nonlinear neutral partial differential equations was discussed. The oscillatory problem of solution to the systems of nonlinear neutral partial differential equations was reduced to the problem to which the neutral differential inequality had not eventual positive solution by using the Green＇s formula and boundary value conditions, and thereby some sufficient conditions were obtained for oscillation of all solutions to such systems under two kinds of different boundary value conditions via the definition of eventually position solution and the method of differential inequalities. These results provide the foundation of mathematical theory for solving the practical problems of physics, biology, engineering and other fields.