一类二阶非线性差分方程的振动性质  

Oscillatory Behavior of Second Order Nonlinear Difference Equation

作　　者：张全信[1] 燕居让[2] 

机构地区：[1]滨州学院数学与信息科学系,山东滨州256603 [2]山西大学数学科学学院,太原030006

出　　处：《工程数学学报》2007年第5期879-884,共6页Chinese Journal of Engineering Mathematics

基　　金：山东省自然科学基金(Y2005A05).

摘　　要：从解的渐近状态着手,将所述方程的所有非平凡解分成互不相交的四类,应用分类讨论方法和分析方法,讨论了一类广泛的二阶非线性差分方程解的振动性质,建立了两个新的振动性定理,推广并改进了已有文献中的相关结果。Starting from the asymptotic behavior of solution, all non-trivial solutions of the second order nonlinear difference equations are divided, in this paper, into four classes which are mutually disjointed. The oscillation nature of a class of extensive second order nonlinear difference equation is discussed by means of the classifying method and analyzing method, Two new oscillation theorems are obtained and the known results in the literature are extended and improved.

关 键 词：二阶 非线性 差分方程 振动性 

分 类 号：O175[理学—数学]