带阻尼项的二阶拟线性微分方程的振动判据  

Oscillation Criteria for the Second-Order Quasi-Linear Differential Equations with Damping

作　　者：金楚华[1] 徐志庭[2] 罗交晚[3] 

机构地区：[1]广东工业大学应用数学学院,广东广州510090 [2]华南师范大学数学学院,广东广州510631 [3]广州大学数学与信息科学学院,广东广州510405

出　　处：《华南理工大学学报（自然科学版）》2005年第6期98-102,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学青年基金资助项目(10301036);湖南省杰出青年基金资助项目(04JJ1001)

摘　　要：籍助于Young不等式和Hld不等式,利用Ricatti变换和H函数的方法,研究了一类拟线性微分方程的振动性,获得了方程的所有解振动的积分条件,推广并改进了最近文献的相关结果.通过适当选取辅助函数H和可以得到一系列具体的振动准则.即使对于不含阻尼项的方程,所得结果也不同于以往的结果.最后给出一个实例以说明主要定理的有效性.With the help of Young inequality and Hld inequality, the oscillatory property of a class of quasi-linear differential equations is investigated by using the Riccati-type transformation and the method of H function. The integral conditions for the oscillation of all the solutions of the equations are also given. Thus, the corresponding results in recent literatures are generalized and improved. By choosing appropriate functions H and  , one can derive a number of explicit oscillation criteria. Even for the equation without damping, the corresponding results are still different from the former ones. An example is finally presented to show the validity of the main theorems.

关 键 词：阻尼项 拟线性微分方程 振动判据 

分 类 号：O175.14[理学—数学]