系数可变号的非线性偏差分方程的频密振动解

Frequently Oscillatory Solutions for a Nonlinear Partial Difference Equation with Variable Coefficients

利用无穷双序列的频密测度概念,讨论了一类系数可变号的非线性偏差分方程的频密振动性.利用方程中系数序列的＂频密测度＂,不仅给出了方程的解频密振动的充分条件,而且指出了解的振动频率.

By applying the concept and the properties of frequency measures of infinite double sequences,the frequently oscillatory behavior of the solutions for the nonlinear partial difference equation with variable coefficients is discussed.Only using the concept of frequency measure of the level sets of the involved parameter sequences in equation,the sufficient conditions of the frequently oscillatory solutions are presented,thus oscillatory frequent of solutions is well described.