二阶微分方程的振动性(英文)  

Oscillation of Second-Order Differential Equations

作　　者：李尚益[1] 

机构地区：[1]娄底师范高等专科学校

出　　处：《山西师范大学学报（自然科学版）》2003年第2期4-10,共7页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：建立了方程 p(t) y′α- 1 y′′+q(t) y a- 1 y=0振动的新准则 .这些准则不同于现有的许多结果 ,仅需 [t0 ,∞ )中一列子区间上的信息 ,而不是整个半直线 .根据斯图姆定理 ,我们的结果更自然并比先前的结果更“Sharp”,且能应用到∫∞t0q(t) dt=-∞的情形 .New oscillation criteria are established for the equation(p(t)y′ α-1 y′)′+q(t)y α-1 y=0that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t 0, ∞), rather than on the whole half line. Our results are more natural according to the sturm separation Theorem and shaper than some previous results, and can be applied to extreme cases such as ∫ ∞ t 0 q(t) d t=-∞. [WTHZ]

关 键 词：二阶微分方程 振动性 振动准则 斯图姆定理 黎卡提变换 拟线性 

分 类 号：O175.7[理学—数学]