非线性双曲方程边值问题的振动准则

目的研究一类具有连续偏差变元的双曲偏泛函微分方程边值问题解的振动性. 方法利用平均化方法,将多维边值问题解的振动性问题转化为常微分方程及其不等式的一维振动问题进行讨论. 结果与结论推广了已有的一类具有离散偏差变元的双曲方程边值问题解的振动性的结果,得到了一类具有连续偏差变元的双曲偏泛函微分方程在两类不同边界条件下解的振动准则.

Oscillatory Criteria for a Class of Boundary Value Problem of Nonlinear Hyperbolic Equations

Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.