一类非线性时滞偏差分方程的频率振动解(英文)  

Frequently oscillatory solutions for nonlinear delay partial difference equations

作　　者：陶元红[1] 李秀东[1] 

机构地区：[1]延边大学理学院,延吉133002

出　　处：《黑龙江大学自然科学学报》2010年第5期591-595,602,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Nature Science Foundation of China(10661011)

摘　　要：利用频率测度的概念,讨论一类带有可变号系数的非线性时滞偏差分方程的解的频率振动性,得到关于解的上度或下度频率振动的振动准则。事实上,关于稳态解的振动的古典概念已经不能准确刻划解的振动性质,因此利用频率测度的概念来描述解的频率振动性是非常必要的。得到的振动准则仅仅利用所讨论方程的系数序列的水平集的"测度"的概念,这不同于以往的文献。不仅得到了方程的解的振动性,而且还准确刻划了解的振动频率。By employing frequency measures,the frequently oscillatory solutions to a class of nonlinear delay partial difference equations with variable coefficients are considered,which may change sign.Some new oscillatory criteria of frequently oscillatory of upper or lower degree are established.Indeed,the usual concept of oscillation of steady state solutions do not catch all their fine details,and it is necessary to use the concept of frequency measures to provide better descriptions.These obtained criteria differ from the classical ones in that they are described by means of the ＂measures＂ of the level sets of the involved parameter sequences.Consequently,main results provide information concerned with how frequent the solutions oscillate.

关 键 词：偏差分方程 频率测度 频率振动解 

分 类 号：O189.1[理学—数学]