系数可变号的非线性偏差分方程ω度频密振动解

ω Degree Frequently Oscillatory Solutions of a Nonlinear Partial Difference Equation with Variable Coefficients

对一类带有可变号系数的非线性偏差分方程的ω度频密振动性问题进行了研究,提出了此类偏差分方程的上/下度ω频密振动性准则.依据无穷双序列的频密测度概念及其性质,深入讨论了此类偏差分方程.仅仅利用方程的系数数列的水平集"频率测度"概念,给出了此类偏差分方程解的上/下度ω频密振动的充分条件,并且准确刻画了解的振动频率.

This paper discuss the to degree frequently oscillatory behavior of the solutions for the nonlinear par- tial difference equation with variable coefficients, proposing some upper or lower to degree oscillatory criteria. By employing the concept and the properties of frequency measures of infinite sequences, such partial difference equa- tion are deeply discussed. Using the concept of ＇ frequency measure＇ of the level sets of the involved parameter se- quences in equation, the sufficient conditions of the solutions of upper or lower to degrees frequently oscillatory are presented, So how frequent the solutions oscillate are well described.